Taking up superspace—what would it take to be a realist about superspace? Supersymmetry is a crucial part of the string theoretic framework for a theory of quantum gravity. Supersymmetric theories (including those outside the context of string theory) present an interesting interpretative challenge. As a result of consistency conditions on the algebra of the supersymmetry (SUSY) generators, one is led to the idea that SUSY, although traditionally defined as a dynamical symmetry between bosons and fermions, could also be thought of as a spacetime symmetry in some extended spacetime, known as superspace. This paper focuses on what it would take to argue for an interpretation that favours the superspace formulation. I introduce a toy model of a supersymmetric field theory and argue for a special case of a more general thesis—that one needs some pre-existing philosophical commitment to favour one mathematical formulation over another. I then consider some extant positions from the literature on the philosophy of spacetime as candidates for such a position in the context of supersymmetric theories.
Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT Abstract: We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the path-integrals. In two dimensional CFTs, this functional is given by the Liouville action. We also formulate the optimization for higher dimensional CFTs and, in various examples, find that the optimized hyperbolic metrics coincide with the time slices of expected gravity duals. Moreover, if we optimize a reduced density matrix, the geometry becomes two copies of the entanglement wedge and reproduces the holographic entanglement entropy. Our approach resembles a continuous tensor network renormalization and provides a concrete realization of the proposed interpretation of AdS/CFT as tensor networks. The present paper is an extended version of our earlier report arXiv:1703.00456 and includes many new results such as evaluations of complexity functionals, energy stress tensor, higher dimensional extensions and time evolutions of thermofield double states.
D–Branes and T–Duality Recent developments in string theory have shown that p–brane solutions and duality symmetries play an important role in understanding the nonperturbative behaviour of the theory. An important example of a duality symmetry is the T–duality [1] which states that a string compactified on a torus with radius R is equivalent to a string compactified on a torus with radius α ′/R where α ′ is the inverse string tension. It turns out that the p–brane solutions whose charge are carried by a RR (Ramond/Ramond) gauge field of the type II supergravity theories have a natural place within open string theory as D–branes [2]. The relation is established via the requirement that the endpoints of the open string are constrained to live on the p+ 1–dimensional worldvolume of the Dirichlet p– brane. Such a (ten–dimensional) open string state is described by Dirichlet boundary conditions for the 9−p transverse directions and Neumann boundary conditions for the p + 1 worldvolume directions. Since under T–duality Dirichlet and Neumann boundary conditions are interchanged it follows that all Dirichlet p–branes (p = 0, · · · , 9) are T-dual versions of each other. A discussion of how this T–duality between D–branes arises in string theory can be found in the recent review article [3]. Since all D–branes are T–dual to each other it is natural to expect that this T–duality is also realized on the underlying p–brane solutions of the IIA/IIB supergravity theories. Furthermore, the T–duality should also be realized on the Dirichlet p–brane actions which act as source terms of the p–brane solutions. It is the purpose of this letter to give the details of this T–duality between Dirichlet p–brane solutions and their source terms and to point out a few subtleties that occur in establishing T–duality.
Timelike duality, M-theory and an exotic form of the Englert solution Through timelike dualities, one can generate exotic versions of M-theory with different spacetime signatures. These are the M∗ -theory with signature (9, 2, −), the M′ -theory, with signature (6, 5, +) and the theories with reversed signatures (1, 10, −), (2, 9, +) and (5, 6, −). In (s, t, ±), s is the number of space directions, t the number of time directions, and ± refers to the sign of the kinetic term of the 3 form. The only irreducible pseudo-riemannian manifolds admitting absolute parallelism are, besides Lie groups, the seven-sphere S 7 ≡ SO(8)/SO(7) and its pseudo-riemannian version S 3,4 ≡ SO(4, 4)/SO(3, 4). [There is also the complexification SO(8, C)/SO(7, C), but it is of dimension too high for our considerations.] The seven-sphere S 7 ≡ S 7,0 has been found to play an important role in 11-dimensional supergravity, both through the Freund-Rubin solution and the Englert solution that uses its remarkable parallelizability to turn on non trivial internal fluxes. The spacetime manifold is in both cases AdS4 ×S 7 . We show that S 3,4 enjoys a similar role in M′ -theory and construct the exotic form AdS4 × S 3,4 of the Englert solution, with non zero internal fluxes turned on. There is no analogous solution in M∗ -theory.
Axion wormholes in AdS compactifications Euclidean wormholes [1–3] are extrema of the action in Euclidean quantum gravity that connect two distant regions, or even two disconnected asymptotic regions. Despite much work over many years it remains unclear whether wormholes can provide valid saddle point contributions to the Euclidean path integral and therefore have physical implications (see e.g. [4–8]). The Weak Gravity Conjecture (WGC) [9] adds a new dimension to this question. This is because its generalization to instantons implies the existence of super-extremal instantons which, when sourced by axions, correspond to Euclidean axion wormholes. It has been argued that such instanton contributions can destroy the flatness of the potential in models of large field inflation based on axions [10], although there is no consensus on this [11]. It is therefore important to elucidate the physical meaning - if any - of wormholes. To this end it is clearly of interest to find wormhole solutions in string theory and in particular in AdS compactifications, where the AdS/CFT dual partition function provides an alternative description of the gravitational path integral. Axionic wormholes [1] provide natural candidates for wormhole solutions in string theory. However axions are always accompanied by dilatons in string theory compactifications, and the existence of regular wormhole solutions depends delicately on the number of scalars and their couplings [4]. In a single axion-dilaton system coupled to gravity, for instance, the dilaton coupling must be sufficiently small in order for wormholes to exist. In [12] Calabi-Yau compactifications were found which allow for regular axionic wormhole solutions in flat space. The situation is more subtle however in compactifications to AdS. Type IIB on AdS5 × S5 does not admit axionic wormholes [5]. On the other hand, in [4] it was argued there are approximate wormhole solutions in Type IIB compactified on AdS3 × S3 × T4. However no clean derivation was given to determine the exact axion - dilaton content of this compactification.1 The validity of those solutions therefore remains somewhat uncertain. Specifically, their smoothness depends on the specific Wick rotation that was used in [4], but it remains unclear whether this particular Wick rotation is the one selected by AdS/CFT. The goal of this paper is to construct exact, regular axionic wormhole solutions in an AdS compactification where the Wick rotation to the Euclidean theory can be made rigorous using AdS/CFT. The wormholes we find are solutions to Euclidean IIB string theory on AdS5 × S5/Zk, whose field theory duals are certain N = 2 quiver theories [13]. The dual operators that are turned on are exactly marginal operators, which enables us to identify the Wick rotation selected by AdS/CFT and therefore rigorously determine the nature of the scalar fields in the theory. Our results further sharpen the paradox with AdS/CFT and the apparent uniqueness of quantum gravity. One is left wondering what is pathological about axionic wormholes.
String Compactification and Global Orientifolded Quivers with Inflation Abstract: We describe global embeddings of fractional D3 branes at orientifolded singularities in type IIB flux compactifications. We present an explicit Calabi-Yau example where the chiral visible sector lives on a local orientifolded quiver while non-perturbative effects, α0 corrections and a T-brane hidden sector lead to full closed string moduli stabilisation in a de Sitter vacuum. The same model can also successfully give rise to inflation driven by a del Pezzo divisor. Our model represents the first explicit Calabi-Yau example featuring both an inflationary and a chiral visible sector.
A Supersymmetric D-Brane Model of Space-Time Foam We present a supersymmetric model of space-time foam with two stacks of eight D8-branes with equal string tensions, separated by a single bulk dimension containing D0-brane particles that represent quantum fluctuations in the space-time foam. The ground-state configuration with static D-branes has zero vacuum energy. However, gravitons and other closed-string states propagating through the bulk may interact with the D0-particles, causing them to recoil and the vacuum energy to become non-zero. This provides a possible origin of dark energy. Recoil also distorts the background metric felt by energetic massless string states, which travel at less than the usual (low-energy) velocity of light. On the other hand, the propagation of chiral matter fields anchored on the D8-branes is not affected by such space-time foam effects.
“Semi-Realistic” F-term Inflation Model Building in Supergravity We describe methods for building “semi-realistic” models of F-term inflation. By semirealistic we mean that they are built in, and obey the requirements of, “semi-realistic” particle physics models. The particle physics models are taken to be effective supergravity theories derived from orbifold compactifications of string theory, and their requirements are taken to be modular invariance, absence of mass terms and stabilization of moduli. We review the particle physics models, their requirements and tools and methods for building inflation models.
Open string T-duality in double space The role of double space is essential in new interpretation of T-duality and consequently in an attempt to construct M-theory. The case of open string is missing in such approach because until now there have been no appropriate formulation of open string T-duality. In the previous paper [1], we showed how to introduce vector gauge fields ANa and ADi at the end-points of open string in order to enable open string invariance under local gauge transformations of the Kalb-Ramond field and its T-dual "restricted general coordinate transformations”. We demonstrated that gauge fields ANa and ADi are T-dual to each other. In the present article we prove that all above results can be interpreted as coordinate permutations in double space.
E(lementary)-Strings in Six-Dimensional Heterotic F-theory Using E-strings, we can analyze not only six-dimensional superconformal field theories but also probe vacua of non-perturabative heterotic string. We study strings made of D3-branes wrapped on various two-cycles in the global F-theory setup. We claim that E-strings are elementary in the sense that various combinations of E-strings can form Mstrings as well as heterotic strings and new kind of strings, called G-strings. Using them, we show that emissions and combinations of heterotic small instantons generate most of known six-dimensional superconformal theories, their affinizations and little string theories. Taking account of global structure of compact internal geometry, we also show that special combinations of E-strings play an important role in constructing six-dimensional theories of D- and E-types. We check global consistency conditions from anomaly cancellation conditions, both from five-branes and strings, and show that they are given in terms of elementary E-string combinations.
On the origin of generalized uncertainty principle from compactified M5-brane In this paper, we demonstrate that compactification in M-theory can lead to a deformation of field theory consistent with the generalized uncertainty principle (GUP). We observe that the matter fields in the M3-brane action contain higher derivative terms. We demonstrate that such terms can also be constructed from a reformulation of the field theory by the GUP. In fact, we will construct the Heisenberg algebra consistent with this deformation, and explicitly demonstrate it to be the Heisenberg algebra obtained from the GUP. Thus, we use compactification in M-theory to motivate for the existence of the GUP.
Target Space Duality in String Theory String theory (see for example [158]) assumes that the elementary particles are one dimensional extended objects rather than point like ones. String theory also comes equipped with a scale associated, nowadays, with the Planck scale (10−33 cm). The standard model describing the color and electro-weak interactions is based on the point particle notion and is successful at the Fermi scale of about 100 Gev (10−16 cm) which is 10−17 smaller than the Planck scale. The correspondence principle requires thus that string theory when applied to these low energies resembles a point particle picture. In fact string theory has an interpretation in terms of point-like field theory whose spectrum consists of an infinity of particles, all except a finite number of which have a mass of the order of the Planck scale. Integrating out the massive modes leads to an effective theory of the light particles. There exists another class of theories whose spectrum consists as well of an infinite tower of particles; this is the Kaluza-Klein type. In such a class of theories [182, 199, 12], gravity is essentially the sole basic interaction, and space-time is assumed to have, in addition to four macroscopic dimensions, extra microscopic dimensions, characterized by some small distance scale. The standard model is assumed to be a low-energy effective action of the light particles resulting from the purely gravitational higher dimensional system. String theory can also be viewed in many cases as representing a space-time with extra dimensions. Nevertheless, the effective low-energy theory, emerging from string theory, turns out to be different from that resulting from a field theory with an infinite number of particles; it possesses many more symmetries. String theory shows also differences when physics is probed at a scale much smaller than the Planck one. In fact, there are various hints that in string theory physics at a very small scale cannot be distinguished from physics at a large scale. A very striking example of that feature is that a string cannot tell if it is propagating on a space-time with one circular dimension of radius R (a dimensionless number) times the Planck scale or 1/R the Planck scale (see figure 1.A). The discrete symmetry apparent in the example is termed target space duality. Moreover, there are indications that string theory possesses an extremely large symmetry of that nature. A study of that symmetry is the subject of the review.
The Disconnect Between Quantum Mechanics and Gravity Abstract: There is a serious disconnect between quantum theory and gravity. It occurs at the level of the very foundations of quantum theory, and is far deeper than just the matter of trying to quantize a non-linear theory. We shall examine some of the physical reasons for this disconnect and show how it manifests itself at the beginning, at the level of the equivalence principle.
No Universe without Big Bang According to Einstein's theory of relativity, the curvature of spacetime was infinite at the big bang. In fact, at this point all mathematical tools fail, and the theory breaks down. However, there remained the notion that perhaps the beginning of the universe could be treated in a simpler manner, and that the infinities of the big bang might be avoided. This has indeed been the hope expressed since the 1980s by the well-known cosmologists James Hartle and Stephen Hawking with their "no-boundary proposal", and by Alexander Vilenkin with his "tunnelling proposal". Now scientists at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute/AEI) in Potsdam and at the Perimeter Institute in Canada have been able to use better mathematical methods to show that these ideas cannot work. The big bang, in its complicated glory, retains all its mystery. One of the principal goals of cosmology is to understand the beginning of our universe. Data from the Planck satellite mission shows that 13.8 billion years ago the universe consisted of a hot and dense soup of particles. Since then the universe has been expanding. This is the main tenet of the hot big bang theory, but the theory fails to describe the very first stages themselves, as the conditions were too extreme. Indeed, as we approach the big bang, the energy density and the curvature grow until we reach the point where they become infinite. As an alternative, the "no-boundary" and "tunneling" proposals assume that the tiny early universe arose by quantum tunnelling from nothing, and subsequently grew into the large universe that we see. The curvature of spacetime would have been large, but finite in this beginning stage, and the geometry would have been smooth - without boundary (see Fig. 1, left panel). This initial configuration would replace the standard big bang. However, for a long time the true consequences of this hypothesis remained unclear. Now, with the help of better mathematical methods, Jean-Luc Lehners, group leader at the AEI, and his colleagues Job Feldbrugge and Neil Turok at Perimeter Institute, managed to define the 35 year old theories in a precise manner for the first time, and to calculate their implications. The result of these investigations is that these alternatives to the big bang are no true alternatives. As a result of Heisenberg's uncertainty relation, these models do not only imply that smooth universes can tunnel out of nothing, but also irregular universes. In fact, the more irregular and crumpled they are, the more likely (see Fig. 1, right panel). "Hence the "no-boundary proposal" does not imply a large universe like the one we live in, but rather tiny curved universes that would collapse immediately", says Jean-Luc Lehners, who leads the "theoretical cosmology" group at the AEI. Hence one cannot circumvent the big bang so easily. Lehners and his colleagues are now trying to figure out what mechanism could have kept those large quantum fluctuations in check under the most extreme circumstances, allowing our large universe to unfold.  
Inflation from Supersymmetry Breaking We explore the possibility that inflation is driven by supersymmetry breaking with the superpartner of the goldstino (sgoldstino) playing the role of the inflaton. Moreover, we impose an R-symmetry that allows to satisfy easily the slow-roll conditions, avoiding the so-called η-problem, and leads to two different classes of small field inflation models; they are characterised by an inflationary plateau around the maximum of the scalar potential, where R-symmetry is either restored or spontaneously broken, with the inflaton rolling down to a minimum describing the present phase of our Universe. To avoid the Goldstone boson and remain with a single (real) scalar field (the inflaton), R-symmetry is gauged with the corresponding gauge boson becoming massive. This framework generalises a model studied recently by the present authors, with the inflaton identified by the string dilaton and R-symmetry together with supersymmetry restored at weak coupling, at infinity of the dilaton potential. The presence of the D-term allows a tuning of the vacuum energy at the minimum. The proposed models agree with cosmological observations and predict a tensor-to-scalar ratio of primordial perturbations 10 − 9 <∼ r <∼ 10 − 4 and an inflation scale 1010 GeV <∼ H ∗ <∼ 1012 GeV. H ∗ may be lowered up to electroweak energies only at the expense of fine-tuning the scalar potential.
Intrinsic Non-Commutativity of Closed String Theory One of the annoying technicalities of string theory is the presence of co-cycles in the physical vertex operators. In the standard account, these co-cycles are required in order to maintain locality on the worldsheet, i.e., to obtain mutual locality of physical vertex insertions. For example, they appear in standard discussions [1] of compactified strings, and rapidly lead to both technical and conceptual issues. In this paper, we re-analyze these issues carefully, and show that the space of string zero modes surprisingly is best interpreted as non-commutative, with the scale of non-commutativity set by α". A by-product of this realization is that the operator algebra becomes straightforward (albeit with a non-commutative product), with no need for co-cycles. This is not inconsistent with our usual notion of space-time in decompactification limits, but it does significantly impact the interpretation of compactifications in terms of local effective field theories. This is a central ingredient that has been overlooked in any of the attempts at duality symmetric formulations of string theory. Indeed, in a follow-up paper we will show that one can obtain a simple understanding of exotic backgrounds such as asymmetric orbifolds [2] and T-folds [3]. Much of the usual space-time interpretation that we use in string theory is built in from the beginning. Its origins, for example, as an S-matrix theory in Minkowski space-time is emblematic of its interpretation in terms of a collection of particle states propagating in a fixed space-time background. We typically view other solutions of string theory in a similar way, with a well-defined distinction between what is big and what is small. Each such case can be viewed as a classical or semi-classical approximation to a deeper quantum theory in which the notion of a given space-time is not built in from the beginning, but is an emergent property of a given classical limit. It is natural to ask under what circumstances a local effective field theory is obtained. Of course, we know many such instances, and we also know many examples where this does not occur, such as cases where non-commutative field theories are thought to emerge. Perhaps the avatar for the absence of a fixed space-time picture is given by duality-symmetric formulations (of which double field theories [4] and our own metastring theory [5–10], are examples). We are in fact working towards a new notion of quantum space-time, in which non-commutativity plays a central role, much as it does in ordinary quantum mechanics. In the present paper then, we uncover an important step towards such an understanding of quantum space-time.
Type IIA D-Branes, K-Theory and Matrix Theory We show that all supersymmetric Type IIA D-branes can be constructed as bound states of a certain number of unstable non-supersymmetric Type IIA D9-branes. This string-theoretical construction demonstrates that D-brane charges in Type IIA theory on spacetime manifold X are classified by the higher K-theory group K−1 (X), as suggested recently by Witten. In particular, the system of N D0-branes can be obtained, for any N, in terms of sixteen Type IIA D9-branes. This suggests that the dynamics of Matrix theory is contained in the physics of magnetic vortices on the worldvolume of sixteen unstable D9-branes, described at low energies by a U(16) gauge theory.
The standard model gauge symmetry from higher-rank unified groups in grand gauge-Higgs unification models We study grand unified models in the five-dimensional space-time where the extra dimension is compactified on S 1/ℤ 2. The spontaneous breaking of unified gauge symmetries is achieved via vacuum expectation values of the extra-dimensional components of gauge fields. We derive one-loop effective potentials for the zero modes of the gauge fields in SU(7), SU(8), SO(10), and E 6 models. In each model, the rank of the residual gauge symmetry that respects the boundary condition imposed at the orbifold fixed points is higher than that of the standard model. We verify that the residual symmetry is broken to the standard model gauge symmetry at the global minima of the effective potential for certain sets of bulk fermion fields in each model.
Superstring Field Theory and the Wess-Zumino-Witten Action We describe a notion of “higher” Wess-Zumino-Witten-like action which is natural in the context of superstring field theories formulated in the large Hilbert space. For the open string, the action is characterized by a pair of commuting cyclic A∞ structures together with a hierarchy of higher-form potentials analogous to the MaurerCartan elements which appear in the conventional Wess-Zumino-Witten action. We apply this formalism to get a better understanding of symmetries of open superstring field theory and the structure of interactions in the Ramond sector, describing an interesting connection between Ramond vertices and Feynman diagrams.  
Unification of Gauge and Yukawa Couplings The discovery of a Higgs boson at the LHC experiments opened a new era in particle physics. Aside from being the last missing particle predicted by the Standard Model (SM), it is allowing a direct probe of the electroweak (EW) symmetry breaking sector of the SM. In particular, the fact that its mass is close to the EW scale itself, has materialised the issue of naturalness. Mass terms for scalar fields are not protected by any quantum symmetry, therefore any new physics sector that couples to it will feed into the value of the mass. In the SM, the EW scale seems to be shielded from high energy scales, like the Planck one, however, no reason for this is present in the SM itself. Another intriguing hint for new physics is the unification of gauge couplings, that occurs at high energies once one takes into account the renormalisation group evolution of the couplings. This has lead to the development of Grand Unified Theories (GUT). The fact that the mass of the top quark is close to the EW scale also suggests that the Yukawa coupling of the top may have a similar origin. The emergence of low-scale extra dimensions [1], mainly supported by string theory constructions, opened new avenues for model building. One of the most interesting idea is developed in Gauge-Higgs Unification (GHU) models [2–4]. Extra dimensional models, in fact, contain a special class of scalar fields, that arise as an additional polarisation of vector gauge fields aligned with the extra compact space. If the Higgs can be identified as such a scalar, its couplings with the fermions (the top quark in particular) are also related to the gauge coupling. In addition, mass terms for the Higgs would be forbidden by gauge invariance in the bulk of the extra dimensions. If the gauge symmetry is suitably broken by boundary conditions, a massless scalar emerges in the spectrum, whose potential is then radiatively generated and finite [5, 6]. The GHU models are rather attractive as they address, at the same time, gauge-Yukawa unification and naturalness.