Marcus K. Benna, Igor R. Klebanov
The first part of these lectures contains an introductory review of the AdS/CFT duality and of its tests. Applications to thermal gauge theory are also discussed briefly. The second part is devoted to a review of gauge-string dualities based on various warped conifold backgrounds, and to their cosmological applications.
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We analyze how string theory dualities may be described in M theory. T dualities arise from scalar-vector dualities in the worldvolume of the membrane of M theory. ``Electric-magnetic'' dualities arise from a duality transformation in M theory compactified on a 3-torus, which takes the membrane into a fivebrane wrapped around the 3-torus.
We construct and fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analyzed from a string theory perspective as tools to deal with open/closed string dualities.
We give simple string theory embeddings of several recently introduced dualities between 2+1-dimensional Chern-Simons matter theories using probe brane holography. Our construction is reliable in the limit of a large number of colors $N$ with fixed Chern-Simons level $k$.
We argue that all conjectured dualities involving various string, M- and F- theory compactifications can be `derived' from the conjectured duality between type I and SO(32) heterotic string theory, T-dualities, and the definition of M- and F- theories. (Based on a talk given at the conference on `Advanced Quantum Field Theory', Le Londe-les-Maures, France, Aug.31-Sept.5, 1996, in memory of Claude Itzykson)
We investigate in the Matrix theory framework, the subgroup of dualities of the DLCQ of M-theory compactified on three-tori, which corresponds to T-duality in the auxiliary Type II string theory. We show how these dualities are realized in the supersymmetric Yang-Mills gauge theories on dual noncommutative three-tori.
We discuss a previous attempt at a microscopic counting of the entropy of asymptotically flat non-extremal black-holes. This method used string dualities to relate 4 and 5 dimensional black holes to the BTZ black hole. We show how the dualities can be justified in a certain limit, equivalent to a near horizon limit, but the resulting spacetime is no longer asymptotically flat.
In this set of lectures I review recent developments in string theory emphasizing their non-perturbative aspects and their recently discovered duality symmetries. The goal of the lectures is to make the recent exciting developments in string theory accessible to those with no previous background in string theory who wish to join the research effort in this area. Topics covered include a brief review of string theory, its compactifications, solitons and D-branes, black hole entropy and web of string dualities. (Lectures presented at ICTP summer school, June 1996)
In this note we study the preservation of the classical pure spinor BRST constraints under super T-duality transformations. We also determine the invariance of the one-loop conformal invariance and of the local gauge and Lorentz anomalies under the super T-dualities.
In the framework of simplicial models, we construct and we fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analysed from a string theory perspective as tools to deal with open/closed string dualities.
This Ph.D. thesis collects results obtained investigating two different aspects of modern unifying theories. In the first part I summarized results achieved investigating simplicial aspects of string dualities. Exploiting Boundary Conformal Field Theory techniques, I investigated the coupling between random Regge triangulations and open string theory, discussing its implications in gauge/gravity correspondence. The second part reports results obtained in the paper hep-th/0309237, devoted to look for cosmological backgrounds of superstring theories.
Dualities among Neveu-Schwarz sector branes in string theory
本文猜想 Neveu-Schwarz 扇区场构成的膜在带通量球面紧致化下存在对偶性，基于弦世界面理论推导出 Chern-Simons 理论的能级-秩对偶，并揭示了 heterotic 弦理论中新膜世界体理论的惊人性质。
Non-Supersymmetric String-String Dualities via Enriques Surfaces
通过恩里克斯曲面实现非超对称的弦-弦对偶性，利用K3表面的商结构构造轨道理论，并与非超对称异弦非对称轨道理论建立双模关系。
An effective action for the M9-brane is proposed. We study its relation with other branes via dualities. Among these, we find actions for branes which are not suggested by the central charges of the Type II superalgebras.
This is the first of a series of papers discussing canonical aspects of the two-dimensional non-linear sigma model in the presence of conformal defects on the world-sheet in the framework of gerbe theory. In the paper, the basic tools of the state-space analysis are introduced, such as the symplectic structure on the state space of the sigma model and the pre-quantum bundle over it, and a relation between the defects and dualities of the sigma model is established. Also, a state-space description of the splitting-joining interaction of the string across the defect is presented, leading to an i…
I review the appearance, within Matrix theory, of the $SL(5,Z)$ U-duality group of M-theory on $T^4$, and the duality between M-theory on K3 and the Heterotic string on $T^3$. In both cases the duality is geometrical and manifest.
We propose a new formalism to study the ABJM matrix model. Contrary to expressing the fractional brane background with the Wilson loops in the open string formalism, we formulate the Wilson loop expectation value from the viewpoint of the closed string background. With this new formalism, we can prove some duality relations in the matrix model.
We study deformations of dualities in finite N=2 supersymmetric QCD. Adding mass terms for some quarks and the adjoint matter to the finite N=2 theory, which is known to have dual descriptions, the correspondence of gauge invariant operators between the original and dual theory is deformed. As a result, we naturally obtain N.Seiberg's N=1 duality. Furthermore, we discuss the origin of the meson and superpotential in the dual theory. This approach can be applied to SU(N), SO(N), and USp(2N) gauge theories, and we analyze all these cases.
The recently found non-critical open string theories is reviewed. These open strings, noncommutative open string theories (NCOS), arise as consistent quantum theories describing the low energy theory of D-branes in a background electric B-field in the critical limit. Focusing on the D3-brane case, we construct the most general (3+1) NCOS, which is described by four parameters. We study S and T -dualities of these theories and argue the existence of a U-duality group.
We describe a general method to determine dualities between supersymmetric 5d gauge theories. The method is based on performing local S-dualities in the geometry associated to the gauge theory. We find that often a duality can be obtained by adding matter to both sides of a more primitive duality. This allows us to define the notion of irreducible dualities which cannot be obtained from more primitive dualities. More general dualities then are obtained by adding matter to both sides of an irreducible duality. The geometric method described in this paper allows us to systematically construct ir…
Flat equivariant gerbes: holonomies and dualities
本研究探讨弦紧致化中平坦规范场和乐选择对应的整体拓扑数据作用，通过引入杂弦Wilson线与II型弦B-field gerbe的非平凡和乐发现世界面对偶性，相关概念方法可推广且对弦对偶性有意义。
We propose dualities of $\mathcal{N} = (0,2)$ supersymmetric boundary conditions for 3d $\mathcal{N} = 2$ gauge theories with orthogonal and symplectic gauge groups. We show that the boundary 't Hooft anomalies and half-indices perfectly match for each pair of the proposed dual boundary conditions.
We show that a class of torsional compactifications of the heterotic string are dual to conventional Kahler heterotic string compactifications. This observation follows from the recently proposed analogue of the c-map for the heterotic string.
We initiate the program of bottom-up derivation of string theory dualities using Swampland principles. In particular, we clarify the relation between Swampland arguments and all the string theory dualities in $d\geq9$ dimensional supersymmetric theories. Our arguments center around the sharpened distance conjecture and rely on various other Swampland principles.
Discovering T-Dualities of Little String Theories
本文提出一种基于曲面几何推断小弦理论圆紧致化T-对偶性的一般方法，适用于非扭曲与扭曲紧致化，并揭示了rank-0小弦理论中的T-对偶及Langlands对偶性。
We examine the properties and symmetries of the lowest order effective theory of 4-dim string backgrounds with axion and dilaton fields and zero cosmological constant. The dimensional reduction yields an O(2,2) current group of transformations in the presence of two commuting Killing symmetries. Special emphasis is placed on the identification of the T and S string duality symmetries, and their intertwining relations. (Contributed to the Proceedings of the Satellite Colloquium "Topology, Strings and Integrable Models" to the XIth International Congress of Mathematical Physics, Paris, 25--28 Ju…
A tubular D3-brane with electromagnetic flux is considered. It is verified that the quantized electric and magnetic charges are the F-string and D-string charges of the brane, respectively. The D3-brane with parallel electric and magnetic fields collapses to the bound state of strings. A D3-brane with nonzero Poynting vector can be viewed as expanded FD strings. A fundamental string is viewed as a collapsed D3-brane and mapped to the (n,m) strings via electric-magnetic duality rotations. This mapping is the same as a weak-strong duality transformation and therefore reveals the equivalence of t…
We present a brief discussion of recent work on duality symmetries in non-trivial string backgrounds. Duality is obtained from a gauged non-linear sigma-model with vanishing gauge field strength. Standard results are reproduced for abelian gauge groups, whereas a new type of duality is identified for non--abelian gauge groups. Examples of duals of WZW models and 4-d black holes are given. (Presented at `From Superstrings to Supergravity', Erice 1992)
This note is supposed to be an introduction to those concepts of toric geometry that are necessary to understand applications in the context of string and F-theory dualities. The presentation is based on the definition of a toric variety in terms of homogeneous coordinates, stressing the analogy with weighted projective spaces. We try to give both intuitive pictures and precise rules that should enable the reader to work with the concepts presented here.
We suggest that the (2,0) six dimensional field theory compactified on $S^1\times K3$ is the Matrix model description of both M-theory on $K3$ and the Heterotic string on $T^3$. This proposal is different from existing proposals for the Heterotic theory. Different limits of the base space geometry give the different space-time interpretations, making M-theory/Heterotic duality manifest. We also present partial results on Heterotic/F-theory duality.
We construct a three dimensional deconfinement method which enables us to find new three-dimensional dualities and we apply various techniques developed in four dimensional supersymmetric gauge theories, such as the product gauge groups and Seiberg-Witten curves to the three dimensional $\mathcal{N}=2$ supersymmetric gauge theories. Dual descriptions of three dimensional $\mathcal{N}=2$ supersymmetric gauge theories which involve two-index matters, for example, adjoint, symmetric, and anti-symmetric matters without superpotentials can be obtained. These matters are described in terms of s-conf…
Duality, the equivalence between seemingly distinct quantum systems, is a curious property that has been known for at least three quarters of a century. In the past two decades it has played a central role in mapping out the structure of theoretical physics. I discuss the unexpected connections that have been revealed among quantum field theories and string theories.
In these lectures we review how some of the recent developments in string theory are closely related to generic properties of supersymmetry. Lectures given at the Nato Advanced Study Institute on "Strings, Branes and Dualities", Cargese, May 26 - June 14, 1997.
We discuss how, by including gauge singlets in supersymmetric gauge theories, one can construct and test new types of duality. This may help in finding dual theories of supersymmetric GUTs. This talk is based on the recent article arXiv:0903.1313 [hep-th].
We systematically study 3d $\mathcal{N}=2$ dualities for $U(N_c)$ gauge theories with different CS levels for the abelian and the non-abelian factors. We derive such dualities by a gauging/ungauging procedure on other known dualities and by adding an opportune CS contact term for the baryonic symmetry. This allows us to follow the various steps on the three sphere partition function, obtaining exact identities among the new dual phases proposed here. We apply the procedure to various cases, namely SQCD without and with adjoint, chiral dualities and some sporadic cases arising from the real mas…
We generalize the construction of four dimensional non-tachyonic orientifolds of type 0B string theory to non-supersymmetric backgrounds. We construct a four dimensional model containing self-dual D3 and D9-branes and leading to a chiral anomaly-free massless spectrum. Moreover, we discuss a further tachyon-free six dimensional model with only D5 branes. Eventually, we speculate about strong coupling dual models of the ten-dimensional orientifolds of type 0B.
S-dualities in scale invariant N=2 supersymmetric field theories with product gauge groups are derived by embedding those theories in asymptotically free theories with higher rank gauge groups. S-duality transformations on the couplings of the scale invariant theory follow from the geometry of the embedding of the scale invariant theory in the Coulomb branch of the asymptotically free theory.
Some relationships between string theories and eleven-dimensional supergravity are discussed and reviewed. We see how some relationships can be derived from others. The cases of N=2 supersymmetry in nine dimensions and N=4 supersymmetry in four dimensions are discussed in some detail. The latter case leads to consideration of quotients of a K3 surface times a torus and to a possible peculiar relationship between eleven-dimensional supergravity and the heterotic strings in ten dimensions. Lecture given at "S-Duality and Mirror Symmetry", Trieste, June 1995.
Buscher duality is a sigma-model duality, implemented by transformation of the target space. Not only in the case of a flat target space, but in a general background, should the Buscher duality reduce to the T-duality familiar in the flat-space string context. We exhibit this reduction explicitly using a pp-wave background as a tractable example. String theory is solved in a compactified Nappi-Witten background and the Buscher-dual theory is likewise solved. The Hamiltonian is computed in both cases, and the results are verified to be T-dual.
We consider interesting Seiberg dualities for $Usp$ gauge theories with an antisymmetric, $8$ fundamentals and no superpotential. We reduce to three dimensions and systematically analyze deformations triggered by real and complex masses, reaching a plethora of $\mathcal{N}\!=\!2$ dualities for $U(N)$ and $Usp(2N)$ gauge theories, possibly with monopole superpotentials and Chern-Simons interactions. Special cases of these "exceptional dualities" are: supersymmetry enhancement dualities, "duality appetizers" and many known dualities relating rank-$1$ gauge groups. The $4d$ $\mathcal{N}\!=\!1$ $U…
Large N topological string dualities have led to a class of proposed open/closed dualities for superstrings. In the topological string context, the worldsheet derivation of these dualities has already been given. In this paper we take the first step in deriving the full ten-dimensional superstring dualities by showing how the dualities arise on the superstring worldsheet at the level of F terms. As part of this derivation, we show for F-term computations that the hybrid formalism for the superstring is equivalent to a $\hat c=5$ topological string in ten-dimensional spacetime. Using the $\hat …
In the fruitful interplay between gauge fields and strings and in many conjectured M-theory dualities, open strings play a prominent role. We review the construction of open-string descendants (un-orientifolds) of closed-string theories admitting a generalized orientation reversal involution. We then specialize the construction to some classes of non-supersymmetric models in D=10 that have been recently considered in the context of duality without supersymmetry. We also discuss the propagation of open and unoriented strings on the NS pentabrane (N5-brane). This background is a prototype of the…
Generalized Dualities for Heterotic and Type I Strings
基于对半极大规范超引力的相容截断，利用heterotic双场理论中的广义Scherk-Schwarz设定定义了heterotic和type I弦的广义对偶性，并显式构造内部几何与规范势以探索新的对偶性与提升。
It is conjectured that the two closed bosonic string theories, Type 0A and Type 0B, correspond to certain supersymmetry breaking orbifold compactifications of M-theory. Various implications of this conjecture are discussed, in particular the behaviour of the tachyon at strong coupling and the existence of non-perturbative fermionic states in Type 0A. The latter are shown to correspond to bound states of Type 0A D-particles, thus providing further evidence for the conjecture. We also give a comprehensive description of the various Type 0 closed and open string theories.
These lectures intend to give a pedagogical introduction into some of the developments in string theory during the last years. They include perturbative T-duality and non perturbative S- and U-dualities, their unavoidable demand for D-branes, an example of enhanced gauge symmetry at fixed points of the T-duality group, a review of classical solitonic solutions in general relativity, gauge theories and tendimensional supergravity, a discussion of their BPS nature, Polchinski's observations that allow to view D-branes as RR charged states in the non perturbative string spectrum, the application …
We discuss non-perturbative corrections to the gauge kinetic functions in a four-dimensional N=2 gauge theory realized with a system of D7/D3-branes in a compactification of type I' theory on T_4/Z_2 x Z_2. The non-perturbative contributions arise when D(-1) branes, corresponding to stringy instantons, are added to the system; such contributions can be explicitly evaluated using localization techniques and precisely match the results predicted by the heterotic/type I' duality. This agreement represents a very non-trivial test of the stringy multi-instanton calculus.
We propose a general method to study open/closed string dualities from transitions in M theory which is valid for a large class of geometrical configurations. By T-duality we can transform geometrically engineered configurations into N = 1 brane configurations and study the transitions of the corresponding branes by lifting the configurations to M-theory. We describe the transformed degenerated M5 branes and extract the field theory information on gluino condensation by factorization of the Seiberg-Witten curve. We also include massive flavors and orientifolds and discuss Seiberg duality which…
We analyze brane dualities in the non-relativistic limit of the worldvolume actions. In particular we have analyzed how the non-relativistic M2-brane is related via these dualities to non-relativistic D2-brane, non-relativistic IIA fundamental string and also, by using T-duality, to non-relativistic D1-string. These actions coincide with ones obtained from relativistic actions by taking non-relativistic limit, showing that the non-relativistic limit and the dualities commute in these cases.
We consider the analogue of Seiberg duality for two-dimensional $N=(2,2)$ gauge theory with orthogonal gauge groups and with fundamental chiral multiplets proposed by Hori. Following Hori, when we consider $O(N)$ gauge group as the (semi)-direct product of $SO(N) \ltimes Z_2$, we have to consider two kinds of the theories $O(N)_{\pm}$ depending on the orbifold action of $Z_2$. We give the evidences for the proposed dualities by working out the elliptic genus of dual pair. The matching of the elliptic genus is worked out perfectly for the proposed dualities.
Starting from a generalization of a recent result on self-duality we systematically analyze self-dual models. We find a criterion to judge whether a given model is self-dual or not. With this tool we construct some new self-dual pairs, focussing on examples with exceptional gauge groups.
A toolkit for ortho-symplectic dualities
本研究提出带与不带单极超势的3维$\n=2$正交规范群理论的新禁闭对偶性，推导需经$\n_2$对称性的规范与希格斯化，可用于解除对称秩2表示场的禁闭，还得到S禁闭对偶性及相关对偶示例与$A_{2N}$ Argyres-Douglas理论的3维镜像。
We extend recent work on the relation of 4d and 3d IR dualities of supersymmetric gauge theories with four supercharges to the case of orthogonal gauge groups. The distinction between different SO(N) gauge theories in 4d plays an important role in this relation. We show that the 4d duality leads to a 3d duality between an SO(N_c) gauge theory with N_f flavors and an SO(N_f-N_c+2) theory with N_f flavors and extra singlets, and we derive its generalization in the presence of Chern-Simons terms. There are two different O(N) theories in 3d, which we denote by O(N)_\pm, and we also show that the O…
The nature of duality symmetries is explored in closed bosonic string theory, particularly in the case of a four-dimensional target space admitting a one-parameter isometry. It appears that the S-duality of string theory behaves analogously to the Ehlers' symmetry of General Relativity. Furthermore, it is demonstrated that the O(1,1) target space duality arising from the isometry interchanges the roles of these two symmetries. The inclusion of the tachyon field is shown to be consistent with T-duality but incompatible with S-duality. Finally, extrapolating to dimensions other than four, the ef…
We work out Seiberg-like dualities for 3d $\mathcal{N}=2$ theories with SU(N) gauge group. We use the $SL(2,\mathbb{Z})$ action on 3d conformal field theories with U(1) global symmetry. One of generator S of $SL(2,\mathbb{Z})$ acts as gauging of the U(1) global symmetry. Utilizing $S=S^{-1}$ up to charge conjugation, we obtain Seiberg-like dual of SU(N) theories by gauging topological U(1) symmetry of the Seiberg-like dual of U(N) theories with the same matter content. We work out the Aharony dualities for SU(N) gauge theory with $N_f$ fundamental/anti-fundamnetal flavors, with/without one adj…
We sharpen the duality between open and closed topological string partition functions for topological gravity coupled to matter. The closed string partition function is a generalised Kontsevich matrix model in the large dimension limit. We integrate out off-diagonal degrees of freedom associated to one source eigenvalue, and find an open/closed topological string partition function, thus proving open/closed duality. We match the resulting open partition function to the generating function of intersection numbers on moduli spaces of Riemann surfaces with boundaries and boundary insertions. More…
Extending recent work on SU gauge theory, we engineer local string models for N=1 four-dimensional SO and USp gauge theories coupled to matter in the fundamental. The local models are type IIB orientifolds with D7 branes on a curved orientifold 7-plane, and matter realized by adding D3 branes on the orientifold plane. The Higgs branches of the SO and USp theories can be matched with the moduli spaces of SO and USp instantons on the compact four-dimensional part of the D7 branes worldvolume. The R-charge of the gauge theories is identified with a U(1) symmetry on the worldvolume of an Euclidean…
We study gauge theories with N=1 supersymmetry in 2+1 dimensions. We start by calculating the 1-loop effective superpotential for matter in an arbitrary representation. We then restrict ourselves to gauge theories with fundamental matter. Using the 1-loop superpotential, we find a universal form for the phase diagrams of many such gauge theories, which is proven to persist to all orders in perturbation theory using a symmetry argument. This allows us to conjecture new dualities for N=1 gauge theories with fundamental matter. We also show that these dualities are related to results in N=2 super…
Abelian dualities and line defect indices for 3d gauge theories
本文通过匹配三维超对称阿贝尔规范理论的线缺陷指标，为BPS线算符对偶性提供证据，并导出适用于圆形与线性箭图规范理论（含SQED、ADHM、ABJM）的新对偶映射。
We compute the cosmological reduction of the fourth powers of the Riemann tensor claimed to arise in string theory at order $α'^{\,3}$, with overall coefficient proportional to $ζ(3)$, and show that it is compatible with an $O(9,9)$ symmetry. This confirms the general result in string theory, due to Sen, that classical string theory with $d$-dimensional translation invariance admits an $O(d,d)$ symmetry to all orders in $α'$.
We examine magnetic and electric near horizon regions of maximally supersymmetric D-brane and NS5-brane bound states and find transformations between near horizon regions with worldvolume dual magnetic and electric fluxes. These point to dual formulations of NCYM, NCOS and OD$p$ theories in the limit of weak coupling and large spatial or temporal non-commutativity length scale in terms of weakly coupled theories with fixed worldvolume dual non-commutativity based on open D-branes. We also examine the strong coupling behavior of the open D-brane theories and propose a unified web of dualities i…
We demonstrate how duality invariance of the low energy expansion of the four-graviton amplitude in type II string theory determines the precise coefficients of multiloop logarithmic ultraviolet divergences of maximal supergravity in various dimensions. This is illustrated by the explicit moduli-dependence of terms of the form D^{2k}R^4, with k<= 3, in the effective action. Furthermore, we show that in the supergravity limit the perturbative contributions are swamped by an accumulation of non-perturbative effects of zero-action instantons.
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