Using T-duality, we will argue that a zero point length exists in the low energy effective field theory of string theory on compactified extra dimensions. Furthermore, if we neglect the oscillator modes, this zero point length would modify low quantum mechanical systems. As this zero length is fixed geometrically, it is important to analyze how it modifies purely quantum mechanical effects. Thus, we will analyze its effects on quantum erasers, because they are based on quantum effects like entanglement. It will be observed that the behavior of these quantum erasers gets modified by this zero point length. As the zero point length is fixed by the radius of compactification, we argue that these results demonstrate a deeper connection between geometry and quantum effects.
We discuss various dual {\it pairs} of $M$-theory compactifications. Each pair consists of a compactification in which the two-brane plays the crucial role in relation to a string theory and a compactification in which the five-brane takes center stage. We show that in many examples such dual pairs are interchanged by the {\it same} duality transformation in each case.
We derive the period structure of several one-modulus Calabi-Yau manifolds. With this knowledge we then obtain the generators of the duality group and the mirror map that defines the physical variable $t$ representing the radius of compactification. We also describe the fundamental region of $t$ and discuss its relation with automorphic functions. As a byproduct of our analysis we compute the non-perturbative corrections of Yukawa couplings.
The duality symmetry group of the cosets ${\textstyle SU(n,1)\over \textstyle SU(n)\otimes U(1)}$, which describe the moduli space of a two-dimensional subspace of an orbifold model with $(n-1)$ complex Wilson lines moduli, is discussed. The full duality group and its explicit action on the moduli fields are derived.
We study the interplay between T-duality, compactification and supersymmetry. We prove that when the original configuration has unbroken space-time supersymmetries, the dual configuration also does if a special condition is met: the Killing spinors of the original configuration have to be independent on the coordinate which corresponds to the isometry direction of the bosonic fields used for duality. Examples of ``losers" (T-duals are not supersymmetric) and ``winners" (T-duals are supersymmetric) are given.
We discuss the spontaneous supersymetry breaking within the low-energy effective supergravity action of four-dimensional superstrings. In particular, we emphasize the non-universality of the soft supersymmetry breaking parameters, the $μ$-problem and the duality symmetries.
The cosmological compactification of D=10, N=1 supergravity-super-Yang-Mills theory obtained from superstring theory is studied. The constraint of unbroken N=1 supersymmetry is imposed. A duality transformation is performed on the resulting consistency conditions. The original equations as well as the transformed equations are solved numerically to obtain new configurations with a nontrivial scale factor and a dynamical dilaton. It is shown that various classes of solutions are possible, which include cosmological solutions with no initial singularity.
We discuss type I -- heterotic duality in four-dimensional models obtained as a Coulomb phase of the six-dimensional U(16) orientifold model compactified on T^2 with arbitrary SU(16) Wilson lines. We show that Kahler potentials, gauge threshold corrections and the infinite tower of higher derivative F-terms agree in the limit that corresponds to weak coupling, large T^2 heterotic compactifications. On the type I side, all these quantities are completely determined by the spectrum of N=2 BPS states that originate from D=6 massless superstring modes.
We review warped compactifications of superstring theory with some attention to the limit in which these resemble "bottom-up" phenomenological models. In addition to some discussion of the original Klebanov-Witten and Klebanov-Strassler set-ups, we also touch on various generalizations of the geometry that have been considered. Various other systems with a holographic duality are also briefly reviewed. The point of this latter exploration is to illustrate how far beyond the standard AdS(5) x S(5) set-up things have moved over the years.
Two classes of stringy instanton effects, stronger than standard field theory instantons, are identified in the heterotic string theory. These contributions are established using type IIA/heterotic and type I/heterotic dualities. They provide examples for the heterotic case of the effects predicted by Shenker based on the large-order behavior of perturbation theory. The corrections vanish as the radius of the compactification goes to infinity. For appropriate amplitudes, they are computable worldsheet or worldline instanton effects on the dual side. Some potential applications are discussed.
In this paper I will further investigate the spectrum of quantum gravity or string theories at large number of dimensions. We will see that volumes of certain orbifolds shrink at large D. It follows that the mass spectra of the leading Kaluza-Klein towers and also of wrapped brane states on these orbifolds possess a non-trivial dependence on D: KK modes become heavy at large D, whereas wrapped branes become light. This observation can be used either to apply the Large Dimension Conjecture or, as we will do, to investigate the possibility of a D-duality symmetry, which relates in gravity compac…
In this note, we discuss electric-magnetic duality between a pair of 4d topological field theories (TQFTs) by considering their compactifications to 2 dimensions. These TQFTs control the long-distance behavior of loop and surface operators in 4d gauge theories with gapped phases. These were recently used in work by S. Gukov and A. Kapustin in detecting phases not distinguishable by the Wilson-'t Hooft criterion and by A. Kapustin and the author to construct discrete theta-angles for lattice Yang-Mills theories. The strong-weak duality is manifested in an exchange of dynamical and background de…
We consider generalised Scherk Schwarz reductions of supergravity and superstring theories with twists by electromagnetic dualities that are symmetries of the equations of motion but not of the action, such as the S-duality of D=4, N=4 super-Yang-Mills coupled to supergravity. The reduction cannot be done on the action itself, but must be done either on the field equations or on a duality invariant form of the action, such as one in the doubled formalism in which potentials are introduced for both electric and magnetic fields. The resulting theory in odd-dimensions has massive form fields sati…
We study N=4 supersymmetric Yang-Mills (SYM) theory with gauge group SU(2) compactified to three dimensions on a circle of circumference beta. The eight fermion terms in the effective action on the Coulomb branch are determined exactly, for all beta, assuming the existence of an interacting Spin(8) invariant fixed point at the origin. The resulting formulae are manifestly invariant under the SL(2,Z) duality of four dimensional N=4 SYM and lead to interesting quantitative predictions for instanton effects in gauge theory and in Type II string theory.
We investigate the lifting of half-maximal four-dimensional gauged supergravities to compactifications of string theory. It is shown that a class of such supergravities can arise from compactifications of IIA string theory on manifolds of SU(2)-structure which may be thought of as K3 fibrations over T^2. Examples of these SU(2)-structure backgrounds, as smooth K3 bundles and as compactifications with H-flux, are given and we also find evidence for a class of non-geometric, Mirror-fold backgrounds. By applying the duality between IIA string theory on K3 and Heterotic string theory on T^4 fibrew…
The moduli spaces of two (0,2) compactifications of the heterotic string can share the same Landau-Ginzburg model even though at large radius they look completely different. It was argued that such a pair of (0,2) models might be connected via a perturbative transition at the Landau-Ginzburg point. Situations of this kind are studied for some explicit models. By calculating the exact dimensions of the generic moduli spaces at large radius, strong indications are found in favor of a different scenario. The two moduli spaces are isomorphic and complex, Kähler and bundle moduli get exchanged.
We present a duality procedure that relates conventional four-dimensional matter-coupled N=1 supergravities to dual formulations in which auxiliary fields are replaced by field-strengths of gauge three-forms. The duality promotes specific coupling constants appearing in the superpotential to vacuum expectation values of the field-strengths. We then apply this general duality to type IIA string compactifications on Calabi-Yau orientifolds with RR fluxes. This gives a new supersymmetric formulation of the corresponding effective four-dimensional theories which includes gauge three-forms.
In the Matrix theories compactified on the $d$ dimensional torus with $d = 5, 6, 7$ which are described by the theories of D$d$-branes in the type IIA or IIB theory on the $d$ dimensional dual torus we analyze the BPS bound states of the background D$d$-brane with other objects by taking the matrix theory limit. Through the Nahm duality transformation the flux and the momentum multiplets for these BPS states are shown to be associated with the black holes and the black strings respectively from the viewpoint of the weakly coupled type IIA string theory compactified on the $d-1$ dimensional tor…
We present a semiclassical calculation of instanton effects in N=4 supersymmetric Yang-Mills theory formulated on R^{3}XS^{1} and also in the N=1 theory obtained by introducing chiral multiplet masses. In the N=4 case, these instanton effects are related to the bulk contribution to the index which counts BPS dyons in the corresponding four dimensional theory. In both cases, the calculations provide semiclassical tests of recently proposed exact results for the lowest non-trivial terms in the derivative expansion of the Wilsonian effective action.
This review talk focusses on some of the interesting developments in the area of superstring compactification that have occurred in the last couple of years. These include the discovery that ``mirror symmetric" pairs of Calabi--Yau spaces, with completely distinct geometries and topologies, correspond to a single (2,2) conformal field theory. Also, the concept of target-space duality, originally discovered for toroidal compactification, is being extended to Calabi--Yau spaces. It also associates sets of geometrically distinct manifolds to a single conformal field theory. A couple of other topi…
We review the construction of open descendants of the type IIB superstring on the Z-orbifold. It results in a chiral four-dimensional model with gauge group $SO(8) \otimes U(12)$ and three generations of matter in the $(8,12^*)\oplus (1,66)$ representations. As a test of type I - heterotic duality, that reduces to a weak/weak duality in D=4, a heterotic model on the same orbifold is also presented. The massless spectrum reproduces exactly the one found in the type I case apart from additional twisted matter charged with respect to the SO(8) gauge group. The puzzle is solved by noting that at g…
These are notes based on lectures given at TASI99. We review the geometry of the moduli space of N=2 theories in four dimensions from the point of view of superstring compactification. The cases of a type IIA or type IIB string compactified on a Calabi-Yau threefold and the heterotic string compactified on K3xT2 are each considered in detail. We pay specific attention to the differences between N=2 theories and N>2 theories. The moduli spaces of vector multiplets and the moduli spaces of hypermultiplets are reviewed. In the case of hypermultiplets this review is limited by the poor state of ou…
The SL(2,R) invaraint ten dimensional type IIB superstring effective action is compactified on a torus to D spacetime dimensions. The transformation properties of scalar, vector and tensor fields, appearing after the dimensional reduction, are obtained in order to maintain the SL(2,R)} invariance of the reduced effective action. The symmetry of the action enables one to generate new string vacua from known configurations. As illustrative examples, new black hole solutions are obtained in five and four dimensions from a given set of solutions of the equations of motion.
Some results are presented concerning duality invariant effective string actions and the construction of automorphic functions for general (2,2) string compactifications. These considerations are applied in order to discuss the {\it minimal} unification of gauge coupling constants in orbifold compactifications with special emphasis on string threshold corrections.
We present a new class of dualities relating non-geometric Calabi-Yau compactifications of type II string theory to T-fold compactifications of the heterotic string, both preserving four-dimensional $\mathcal{N}=2$ supersymmetry. The non-geometric Calabi-Yau space is a $K3$ fibration over $T^2$ with non-geometric monodromies in the duality group $O(Γ_{4,20})$; this is dual to a heterotic reduction on a $T^4$ fibration over $T^2$ with the $O(Γ_{4,20})$ monodromies now viewed as heterotic T-dualities. At a point in moduli space which is a minimum of the scalar potential, the type II compactifica…
To obtain a unified framework for symmetric and asymmetric heterotic orbifold constructions we provide a systematic study of Narain compactifications orbifolded by finite order T-duality subgroups. We review the generalized vielbein that parametrizes the Narain moduli space (i.e. the metric, the B-field and the Wilson lines) and introduce a convenient basis of generators of the heterotic T-duality group. Using this we generalize the space group description of orbifolds to Narain orbifolds. This yields a unified, crystallographic description of the orbifold twists, shifts as well as Narain modu…
We investigate a simple class of type II string compactifications which incorporate nongeometric "fluxes" in addition to "geometric flux" and the usual H-field and R-R fluxes. These compactifications are nongeometric analogues of the twisted torus. We develop T-duality rules for NS-NS geometric and nongeometric fluxes, which we use to construct a superpotential for the dimensionally reduced four-dimensional theory. The resulting structure is invariant under T-duality, so that the distribution of vacua in the IIA and IIB theories is identical when nongeometric fluxes are included. This gives a …
Many important ideas about string duality that appear in conventional $\T^2$ compactification have analogs for $\T^2$ compactification without vector structure. We analyze some of these issues and show, in particular, how orientifold planes associated with $Sp(n)$ gauge groups can arise from T-duality and how they can be interpreted in F-theory. We also, in an appendix, resolve a longstanding puzzle concerning the computation of $\Tr (-1)^F$ in four-dimensional supersymmetric Yang-Mills theory with gauge group SO(n).
We investigate compactifications with duality twists and their relation to orbifolds and compactifications with fluxes. Inequivalent compactifications are classified by conjugacy classes of the U-duality group and result in gauged supergravities in lower dimensions with nontrivial Scherk-Schwarz potentials on the moduli space. For certain twists, this mechanism is equivalent to introducing internal fluxes but is more general and can be used to stabilize some of the moduli. We show that the potential has stable minima with zero energy precisely at the fixed points of the twist group. In string …
We study 2+1D toroidal compactifications of M-theory with twists in the U-duality group. These compactifications realize many symmetric-manifolds from the classification of 2+1D extended supergravity moduli-spaces. We then focus on the moduli-space $SU(2,1)/U(2)$ obtained by dimensional reduction of pure N=2 supergravity in 3+1D. This space is realized with an explicit example. Assuming that there are no quantum corrections, we conjecture that the classical discrete duality group has to be augmented with an extra strong/weak coupling duality. This implies the existence of new phases of the the…
Using U-duality, the properties of the matrix theories corresponding to the compactification of M-theory on $T^d$ are investigated. The couplings of the $d+1$ dimensional effective Super-Yang-Mills theory to all the M-theory moduli is deduced and the spectrum of BPS branes in the SYM gives the corresponding spectrum of the matrix theory.Known results are recovered for $d\le 5$ and predictions for $d>5$ are proposed. For $d>3$, the spectrum includes $d-4$ branes arising from YM instantons, and U-duality interchanges momentum modes with brane wrapping modes.For $d=6$, there is a generalised $þ$-…
Oscillating moduli fields can support a cosmological scaling solution in the presence of a perfect fluid when the scalar field potential satisfies appropriate conditions. We examine when such conditions arise in higher-dimensional, non-linear sigma-models that are reduced to four dimensions under a generalized Scherk-Schwarz compactification. We show explicitly that scaling behaviour is possible when the higher-dimensional action exhibits a global SL(n,R) or O(2,2) symmetry. These underlying symmetries can be exploited to generate non-trivial scaling solutions when the moduli fields have non-c…
We derive a formula for D3-brane charge on a compact spacetime, which includes torsion corrections to the tadpole cancellation condition. We use this to classify D-branes and RR fluxes in type II string theory on RP^3xRP^{2k+1}xS^{6-2k} with torsion H-flux and to demonstrate the conjectured T-duality to S^3xS^{2k+1}xS^{6-2k} with no flux. When k=1, H\neq 0 and so the K-theory that classifies fluxes is twisted. When k=2 the square of the H-flux yields an S-dual Freed-Witten anomaly which is canceled by a D3-brane insertion that ruins the K-theory classification. When k=3 the cube of H is nontri…
A general formula for the topology and H-flux of the T-duals of type II string theories with H-flux on toroidal compactifications is presented here. It is known that toroidal compactifications with H-flux do not necessarily have T-duals which are themselves toroidal compactifications. A big puzzle has been to explain these mysterious ``missing T-duals'', and our paper presents a solution to this problem using noncommutative topology. We also analyze the T-duality group and its action, and illustrate these concepts with examples.
We obtain the bosonic Lagrangians of vector and hypermultiplets coupled to four-dimensional $\mathcal{N}=2$ supergravity in signatures $(0,4)$, $(1,3)$ and (2,2) by compactification of type-II string theories in signatures (0,10), (1,9) and (2,8) on a Calabi-Yau threefold. Depending on the signature and the distinctions between type-IIA/IIA$^*$/IIB/IIB$^*$/IIB' the resulting scalar geometries are special Kähler or special para-Kähler for vector multiplets and quaternion-Kähler or para-quaternion Kähler for hypermultiplets. By spacelike and timelike reductions we obtain three-dimensional $\math…
Global aspects of Scherk-Schwarz dimensional reduction are discussed and it is shown that it can usually be viewed as arising from a compactification on the compact space obtained by identifying a (possibly non-compact) group manifold G under a discrete subgroup Gamma, followed by a truncation. This allows a generalisation of Scherk-Schwarz reductions to string theory or M-theory as compactifications on G/Gamma, but only in those cases in which there is a suitable discrete subgroup of G. We analyse such compactifications with flux and investigate the gauge symmetry and its spontaneous breaking…
We discuss non-perturbative aspects of string effective field theories with N=1 supersymmetry in four dimensions. By the use of a scalar potential, which is on-shell invariant under the supersymmetric duality of the dilaton, we study gaugino condensation in (2,2) symmetric Z_{N} orbifold compactifications. The duality under consideration relates a two-form antisymmetric tensor to a pseudoscalar. We show, that our approach is independent of the superfield-representation of the dilaton and preserves the U(1)_{PQ} Peccei-Quinn symmetry exactly.
A massive version of T-duality in six dimensions is given, that maps the K3 compactification of Romans' theory onto the K3 compactification of Type IIB theory. This is done by performing a (standard) Kaluza-Klein reduction on six-dimensional massive Type IIA and a Scherk-Schwarz reduction on Type IIB, mapping both theories onto the same five-dimensional theory. We also comment shortly on the difficulties arising if one intends to construct a massive generalisation of the six-dimensional string-string duality.
We study the duality between four-dimensional N=2 compactifications of heterotic and type IIA string theories. Via adiabatic fibration of the duality in six dimensions, type IIA string theory compactified on a K3-fibred Calabi-Yau threefold has a potential heterotic dual compactification. This adiabatic picture fails whenever the K3 fibre degenerates into multiple components over points in the base of the fibration. Guided by monodromy, we identify such degenerate K3 fibres as solitons generalizing the NS5-brane in heterotic string theory. The theory of degenerations of K3 surfaces can then be…
I discuss the role of spacetime supersymmetry in the interplay between strong/weak coupling duality and target space duality in string theory which arises in string/string duality. This can be seen via the construction of string soliton solutions which in $N=4$ compactifications of heterotic string theory break more than $1/2$ of the spacetime supersymmetries but whose analogs in $N=2$ and $N=1$ compactifications break precisely $1/2$ of the spacetime supersymmetries. As a result, these solutions may be interpreted as stable solitons in the latter two cases, and correspond to Bogomol'nyi-satur…
On compactification to six spacetime dimensions, the fundamental heterotic string admits as a soliton a dual string whose effective worldsheet action couples to the background fields of the dual formulation of six-dimensional supergravity. On further toroidal compactification to four spacetime dimensions, the dual string acquires an $O(2,2;Z)$ target-space duality. This contains as a subgroup the axion-dilaton $SL(2,Z)$ which corresponds to a strong/weak coupling duality for the fundamental string. The dual string also provides a new non-perturbative mechanism for enhancement of the gauge symm…
A rich pattern of gauge symmetries is found in the moduli space of heterotic string toroidal compactifications, at fixed points of the T-duality transformations. We analyze this pattern for generic tori, and scrutinize in full detail compactifications on a circle, where we find all the maximal gauge symmetry groups and the points where they arise. We show the gauge symmetry groups that arise at special points, in figures of slices of the 17-dimensional moduli space of Wilson lines and circle radii. We then study the target space realization of the duality symmetry. Although the global continuo…
We study the implications of duality symmetry on the analyticity properties of the partition function as it depends upon the compactification length. In order to obtain non-trivial compactifications, we give a physical prescription to get the Helmholtz free energy for any heterotic string supersymmetric or not. After proving that the free energy is always invariant under the duality transformation $R\rightarrow α^{'}/(4R)$ and getting the zero temperature theory whose partition function corresponds to the Helmholtz potential, we show that the self-dual point $R_{0}=\sqrt{α^{'}}/2$ is a generic…
The free (4,0) superconformal theory in 6 dimensions and its toroidal dimensional reductions are studied. The reduction to four dimensions on a 2-torus has an $SL(2,\Z)$ duality symmetry that acts non-trivially on the linearised gravity sector, interchanging the linearised Einstein equations and Bianchi identities and giving a self-duality between strong and weak coupling regimes. The possibility of this extending to an interacting form of the theory is discussed and implications for the non-geometric picture of gravity that could emerge are considered.
We discuss a duality of (0,2) heterotic string vacua which implies that certain pairs of (0,2) Calabi-Yau compactifications on topologically distinct target manifolds yield identical string theories. Some complex structure moduli in one model are interpreted in the dual model as deforming the holomorphic structure of the vacuum gauge bundle (and vice versa). A better understanding of singularity resolution for (0,2) models may reveal that this duality of compactifications on singular spaces is part of a larger story, involving smooth topology-changing processes which interpolate between the (0…
In the warped compactification with a single Randall-Sundrum brane, a puzzling claim has been made that scalar fields can be bound to the brane but their Hodge dual higher-rank anti-symmetric tensors cannot. By explicitly requiring the Hodge duality, a prescription to resolve this puzzle was recently proposed by Duff and Liu. In this note, we implement the Hodge duality via path integral formulation in the presence of the background gravity fields of warped compactifications. It is shown that the prescription of Duff and Liu can be naturally understood within this framework.
Using a $U$-duality symmetry of type II compactification on $T^4$ represented by triality action on the $T$-duality group, and applying the adiabatic argument we construct dual pairs of type II compactifications in lower dimensions. The simplicity of this construction makes it an ideal set up for testing various conjectures about string dualities. In some of these models the type II string has a perturbative non-abelian gauge symmetry. Examples include models with $N=2,4,6$ supersymmetry in four dimensions. There are also self-dual (in the sense of $S-T$ exchange symmetric) $N=2$ and $N=6$ exa…
Using heterotic/type II string duality, we obtain exact nonperturbative results for the point particle limit (alpha' -> 0) of some particular four dimensional, N=2 supersymmetric compactifications of heterotic strings. This allows us to recover recent exact nonperturbative results on N=2 gauge theory directly from tree-level type II string theory, which provides a highly non-trivial, quantitative check on the proposed string duality. We also investigate to what extent the relevant singular limits of Calabi-Yau manifolds are related to the Riemann surfaces that underlie rigid N=2 gauge theory.
The four-dimensional N=1 effective action of F-theory compactified on a Calabi-Yau fourfold is studied by lifting a three-dimensional M-theory compactification. The lift is performed by using T-duality realized via a Legendre transform on the level of the effective action, and the application of vector-scalar duality in three dimensions. The leading order Kahler potential and gauge-kinetic coupling functions are determined. In these compactifications two sources of gauge theories are present. Space-time filling non-Abelian seven-branes arise at the singularities of the elliptic fibration of th…
The purpose of this article is to present a pedagogical review of T-dualityin in string theory. The evolution of the closed string is envisaged on the worldsheet in the presence of its massless excitations. The duality symmetry is studied when some of the spacial coordinates are compactified on d-dimensional torus, $T^d$. The known results are reviewed to elucidate that equations of motion for the compact coordinates are $O(d,d)$ covariant, $d$ being the number of compact directions. Next, the vertex operators of excited massive levels are considered in a simple compactification scheme. It is …
We consider $E_8\times E_8$ heterotic compactifications on $K3$ and $K3\times T^2$. The idea of heterotic/heterotic duality in $D=6$ has difficulties for generic compactifications since for large dilaton values some gauge groups acquire negative kinetic terms. Recently Duff, Minasian and Witten (DMW) suggested a solution to this problem which only works if the compactification is performed assuming the presence of symmetric gauge embeddings on both $E_8$'s. We consider an alternative in which asymmetric embeddings are possible and the wrong sign of kinetic terms for large dilaton value is a si…
We begin by presenting a symmetric version of the circle equivariant T-duality result in a joint work of the second author with Siye Wu, thereby generalising the results there. We then initiate the study of twisted equivariant Courant algebroids and equivariant generalised geometry and apply it to our context. As before, T-duality exchanges type II A and type II B string theories. In our theory, both spacetime and the T-dual spacetime can be singular spaces when the fixed point set is non-empty; the singularities correspond to Kaluza-Klein monopoles. We propose that the Ramond-Ramond charges o…
The nature of M-theory on K3 X I, where I is a line interval, is considered, with a view towards formulating a `matrix theory' representation of that situation. Various limits of this compactification of M-theory yield a number of well known N=1 six dimensional compactifications of the heterotic and type I string theories. Geometrical relations between these limits give rise to string/string dualities between some of these compactifications. At a special point in the moduli space of compactifications, this motivates a partial definition of the matrix theory representation of the M-theory on K3…
In this short paper we look at the action of T-duality and string duality groups on fermions, in maximally-supersymmetric theories and related theories. Briefly, we argue that typical duality groups such as SL(2,Z) have sign ambiguities in their actions on fermions, and propose that pertinent duality groups be extended by Z_2, to groups such as the metaplectic group. Specifically, we look at duality groups arising from mapping class groups of tori in M theory compactifications, T-duality, ten-dimensional type IIB S-duality, and (briefly) four-dimensional N=4 super Yang-Mills, and in each case,…
We show that the full global symmetry groups of all the D-dimensional maximal supergravities can be described in terms of the closure of the internal general coordinate transformations of the toroidal compactifications of D=11 supergravity and of type IIB supergravity, with type IIA/IIB T-duality providing an intertwining between the two pictures. At the quantum level, the part of the U-duality group that corresponds to the surviving discretised internal general coordinate transformations in a given picture leaves the internal torus invariant, while the part that is not described by internal g…
We study the low-energy limit of a compactification of N=4 U(n) super Yang-Mills theory on $S^1$ with boundary conditions modified by an S-duality and R-symmetry twist. This theory has N=6 supersymmetry in 2+1D. We analyze the $T^2$ compactification of this 2+1D theory by identifying a dual weakly coupled type-IIA background. The Hilbert space of normalizable ground states is finite-dimensional and appears to exhibit a rich structure of sectors. We identify most of them with Hilbert spaces of Chern-Simons theory (with appropriate gauge groups and levels). We also discuss a realization of a rel…
We find evidence for a duality between the standard matrix formulations of M theory and a background independent theory which extends loop quantum gravity by replacing SU(2) with a supersymmetric and quantum group extension of SU(16). This is deduced from the recently proposed cubic matrix model for M theory which has been argued to have compactifications which reduce to the IKKT and dWHN-BFSS matrix models. Here we find new compactifications of this theory whose Hilbert spaces consist of SU(16) conformal blocks on compact two-surfaces. These compactifications break the SU(N) symmetry of the s…
We study the effect of quantum corrections on heterotic compactifications on elliptic fibrations away from the stable degeneration limit, elaborating on a recent observation by Malmendier and Morrison. We show that already for the simplest non-trivial elliptic fibration the effect is quite dramatic: the $I_1$ degeneration with trivial gauge background dynamically splits into two T-fects with monodromy around each T-fect being (conjugate to) T-duality along one of the legs of the $T^2$. This implies that almost every elliptic heterotic compactification becomes a non-geometric T-fold away from t…
Compactifications in duality covariant constructions such as generalised geometry and double field theory have proven to be suitable frameworks to reproduce gauged supergravities containing non-geometric fluxes. However, it is a priori unclear whether these approaches only provide a reformulation of old results, or also contain new physics. To address this question, we classify the T- and U-duality orbits of gaugings of (half-)maximal supergravities in dimensions seven and higher. It turns out that all orbits have a geometric supergravity origin in the maximal case, while there are non-geometr…
