arXiv subjects

Anton Kapustin

Publications and source records attributed to Anton Kapustin.

At least 109 records · Page 6Linked to original sources

arXiv2003

Noncritical Superstrings in a Ramond-Ramond Background

We use the recently found matrix description of noncritical superstring theory of Type 0A to compute tachyon scattering amplitudes in a background with a RR flux. We find that after the string coupling is multiplicatively renormalized, the amplitudes in any genus become polynomial in the RR flux. We propose that in the limit where both the string coupling and the RR flux go to infinity, the theory has a weakly-coupled description in terms of another superstring theory with a vanishingly small RR flux. This duality exchanges the inverse string coupling and the 0-brane charge. The dual superstring theory must have a peculiar property that its only field-theoretic degree of freedom is a massless RR scalar.

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arXiv2003

D-branes in Topological Minimal Models: the Landau-Ginzburg Approach

We study D-branes in topologically twisted N=2 minimal models using the Landau-Ginzburg realization. In the cases of A and D-type minimal models we provide what we believe is an exhaustive list of topological branes and compute the corresponding boundary OPE algebras as well as all disk correlators. We also construct examples of topological branes in E-type minimal models. We compare our results with the boundary state formalism, where possible, and find agreement.

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arXiv2002

D-Branes in Landau-Ginzburg Models and Algebraic Geometry

We study topological D-branes of type B in N=2 Landau-Ginzburg models, focusing on the case where all vacua have a mass gap. In general, tree-level topological string theory in the presence of topological D-branes is described mathematically in terms of a triangulated category. For example, it has been argued that B-branes for an N=2 sigma-model with a Calabi-Yau target space are described by the derived category of coherent sheaves on this space. M. Kontsevich previously proposed a candidate category for B-branes in N=2 Landau-Ginzburg models, and our computations confirm this proposal. We also give a heuristic physical derivation of the proposal. Assuming its validity, we can completely describe the category of B-branes in an arbitrary massive Landau-Ginzburg model in terms of modules over a Clifford algebra. Assuming in addition Homological Mirror Symmetry, our results enable one to compute the Fukaya category for a large class of Fano varieties. We also provide a (somewhat trivial) counter-example to the hypothesis that given a closed string background there is a unique set of D-branes consistent with it.

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arXiv2002

Topological Disorder Operators in Three-Dimensional Conformal Field Theory

Many abelian gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories which are not polynomial in the fundamental fields and create topological disorder. They can be regarded as higher-dimensional analogues of twist and winding-state operators in free 2d CFTs. We call them monopole operators for reasons explained in the text. The importance of monopole operators is that in the Higgs phase, they create Abrikosov-Nielsen-Olesen vortices. We study properties of these operators in three-dimensional QED using large N_f expansion. In particular, we show that monopole operators belong to representations of the conformal group whose primaries have dimension of order N_f. We also show that monopole operators transform non-trivially under the flavor symmetry group, with the precise representation depending on the value of the Chern-Simons coupling.

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arXiv2002

Monopole Operators and Mirror Symmetry in Three Dimensions

We study vortex-creating, or monopole, operators in 3d CFTs which are the infrared limit of N=2 and N=4 supersymmetric QEDs in three dimensions. Using large-Nf expansion, we construct monopole operators which are primaries of short representations of the superconformal algebra. Mirror symmetry in three dimensions makes a number of predictions about such operators, and our results confirm these predictions. Furthermore, we argue that some of our large-Nf results are exact. This implies, in particular, that certain monopole operators in N=4 d=3 SQED with Nf=1 are free fields. This amounts to a proof of 3d mirror symmetry in a special case.

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arXiv2002

Worldsheet Descriptions of Wrapped NS Five-Branes

We provide a world-sheet description of Neveu-Schwarz five-branes wrapped on a complex projective space. It is an orbifold of the product of an N=2 minimal model and the IR fixed point of a certain linear sigma model. We show how the naked singularity in the supergravity description is resolved by the world-sheet CFT. Applying mirror symmetry, we show that the low-energy theory of NS5-branes wrapped on CP^1 in Eguchi-Hanson space is described by the Seiberg-Witten prepotential for N=2 super-Yang-Mills, with the gauge group given by the ADE-type of the five-brane. The world-sheet CFT is generically regular, but singularities develop precisely at the Argyres-Douglas points and massless monopole points of the space-time theory. We also study the low-energy theory of NS5-branes wrapped on CP^2 in a Calabi-Yau 3-fold and its relation to (2,2) super-Yang-Mills theory in two dimensions.

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arXiv2002

Hyperkahler Metrics from Periodic Monopoles

Relative moduli spaces of periodic monopoles provide novel examples of Asymptotically Locally Flat hyperkahler manifolds. By considering the interactions between well-separated periodic monopoles, we infer the asymptotic behavior of their metrics. When the monopole moduli space is four-dimensional, this construction yields interesting examples of metrics with self-dual curvature (gravitational instantons). We discuss their topology and complex geometry. An alternative construction of these gravitational instantons using moduli spaces of Hitchin equations is also described.

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arXiv2001

Vertex Algebras, Mirror Symmetry, And D-Branes: The Case Of Complex Tori

A vertex algebra is an algebraic counterpart of a two-dimensional conformal field theory. We give a new definition of a vertex algebra which includes chiral algebras as a special case, but allows for fields which are neither meromorphic nor anti-meromorphic. To any complex torus equipped with a flat Kahler metric and a closed 2-form we associate an N=2 superconformal vertex algebra (N=2 SCVA) in the sense of our definition. We find a criterion for two different tori to produce isomorphic N=2 SCVA's. We show that for algebraic tori isomorphism of N=2 SCVA's implies the equivalence of the derived categories of coherent sheaves corresponding to the tori or their noncommutative generalizations (Azumaya algebras over tori). We also find a criterion for two different tori to produce N=2 SCVA's related by a mirror morphism. If the 2-form is of type (1,1), this condition is identical to the one proposed by Golyshev, Lunts, and Orlov, who used an entirely different approach inspired by the Homological Mirror Symmetry Conjecture of Kontsevich. Our results suggest that Kontsevich's conjecture must be modified: coherent sheaves must be replaced with modules over Azumaya algebras, and the Fukaya category must be ``twisted'' by a closed 2-form. We also describe the implications of our results for BPS D-branes on Calabi-Yau manifolds.

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arXiv2001

Remarks on A-branes, Mirror Symmetry, and the Fukaya category

We discuss D-branes of the topological A-model (A-branes), which are believed to be closely related to the Fukaya category. We give string theory arguments which show that A-branes are not necessarily Lagrangian submanifolds in the Calabi-Yau: more general coisotropic branes are also allowed, if the line bundle on the brane is not flat. We show that a coisotropic A-brane has a natural structure of a foliated manifold with a transverse holomorphic structure. We argue that the Fukaya category must be enlarged with such objects for the Homological Mirror Symmetry conjecture to be true.

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arXiv2001

Duality of the Fermionic 2d Black Hole and N=2 Liouville Theory as Mirror Symmetry

We prove the equivalence of the SL(2,R)/U(1) Kazama-Suzuki model, which is a fermionic generalization of the 2d Black Hole, and N=2 Liouville theory. We show that this duality is an example of mirror symmetry. The essential part of the derivation is to realize the fermionic 2d Black Hole as the low energy limit of a gauged linear sigma-model. Liouville theory is obtained by dualizing the charged scalar fields and taking into account the vortex-instanton effects, as proposed recently in non-dilatonic models. The gauged linear sigma-model we study has many useful generalizations which we briefly discuss. In particular, we show how to construct a variety of dilatonic superstring backgrounds which generalize the fermionic 2d Black Hole and admit a mirror description in terms of Toda-like theories.

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arXiv2000

Periodic Monopoles With Singularities And N=2 Super-QCD

We study solutions of the Bogomolny equation on R^2\times S^1$ with prescribed singularities. We show that Nahm transform establishes a one-to-one correspondence between such solutions and solutions of the Hitchin equations on a punctured cylinder with the eigenvalues of the Higgs field growing at infinity in a particular manner. The moduli spaces of solutions have natural hyperkahler metrics of a novel kind. We show that these metrics describe the quantum Coulomb branch of certain N=2 d=4 supersymmetric gauge theories on R^3\times S^1. The Coulomb branches of the corresponding uncompactified theories have been previously determined by E. Witten using the M-theory fivebrane. We show that the Seiberg-Witten curves of these theories are identical to the spectral curves associated to solutions of the Bogomolny equation on R^2\times S^1. In particular, this allows us to rederive Witten's results without recourse to the M-theory fivebrane.

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arXiv2000

Nahm Transform For Periodic Monopoles And N=2 Super Yang-Mills Theory

We study Bogomolny equations on $R^2\times S^1$. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using Nahm transform, we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperkähler manifolds and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of $k$ periodic monopoles provides the exact solution of ${\cal N}=2$ super Yang-Mills theory with gauge group $SU(k)$ compactified on a circle of arbitrary radius.

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arXiv2000

Noncommutative Instantons and Twistor Transform

Recently N.Nekrasov and A.Schwarz proposed a modification of the ADHM construction of instantons which produces instantons on a noncommutative deformation of the 4-dimensional real affine space. In this paper we study the relation between their construction and algebraic bundles on noncommutative projective spaces. We exhibit one-to-one correspondences between three classes of objects: framed bundles on a noncommutative projective plane, certain complexes of sheaves on a noncommutative 3-dimensional projective space, and the modified ADHM data. The modified ADHM construction itself is interpreted in terms of a noncommutative version of the twistor transform. We also prove that the moduli space of framed bundles on the noncommutative projective plane has a natural hyperkahler metric and is isomorphic as a hyperkahler manifold to the moduli space of framed torsion free sheaves on the commutative projective plane. The natural complex structures on the two moduli spaces do not coincide but are related by an SO(3) rotation. Finally, we propose a construction of instantons on a more general noncommutative R^4 than the one considered by Nekrasov and Schwarz (a q-deformed R^4).

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arXiv2000

On The Universality Class Of Little String Theories

We propose that Little String Theories in six dimensions are quasilocal quantum field theories. Such field theories obey a modification of Wightman axioms which allows Wightman functions (i.e. vacuum expectation values of products of fundamental fields) to grow exponentially in momentum space. Wightman functions of quasilocal fields in x-space violate microlocality at short distances. With additional assumptions about the ultraviolet behavior of quasilocal fields, one can define approximately local observables associated to big enough compact regions. The minimum size of such a region can be interpreted as the minimum distance which observables can probe. We argue that for Little String Theories this distance is of order {\sqrt N}/M_s.

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arXiv1999

D-branes in a topologically nontrivial B-field

We study global worldsheet anomalies for open strings ending on several coincident D-branes in the presence of a B-field. We show that cancellation of anomalies is made possible by a correlation between the t'Hooft magnetic flux on the D-branes and the topological class of the B-field. One application of our results is a proper understanding of the geometric nature of the gauge field living on D-branes: rather than being a connection on a vector bundle, it is a connection on a module over a certain noncommutative algebra. Our argument works for a general closed string background. We also explain why in the presence of a topologically nontrivial B-field whose curvature is pure torsion D-branes represent classes in a twisted K-theory, as conjectured by E. Witten.

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arXiv1999

Heterotic Little String Theories and Holography

It has been conjectured that Little String Theories in six dimensions are holographic to critical string theory in a linear dilaton background. We test this conjecture for theories arising on the worldvolume of heterotic fivebranes. We compute the spectrum of chiral primaries in these theories and compare with results following from Type I-heterotic duality and the AdS/CFT correspondence. We also construct holographic duals for heterotic fivebranes near orbifold singularities. Finally we find several new Little String Theories which have Spin(32)/Z_2 or E_8 \times E_8 global symmetry but do not have a simple interpretation either in heterotic or M-theory.

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arXiv1999

D_k Gravitational Instantons and Nahm Equations

We construct D_k asymptotically locally flat gravitational instantons as moduli spaces of solutions of Nahm equations. This allows us to find their twistor spaces and Kahler potentials.

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arXiv1999

N=1 Theories, T-duality, and AdS/CFT correspondence

We construct an N=1 superconformal field theory using branes of type IIA string theory. The IIA construction is related via T-duality to a IIB configuration with 3-branes in a background generated by two intersecting O7-planes and 7-branes. The IIB background can be viewed as a local piece of an F-theory compactification previously studied by Sen in connection with the Gimon-Polchinski orientifold. We discuss the deformations of the IIA and IIB constructions and describe a new supersymmetric configuration with curving D6-branes. Starting from the IIB description we find the supergravity dual of the large N field theory and discuss the matching of operators and KK states. The matching of non-chiral primaries exhibits some interesting new features. We also discuss a relevant deformation of the field theory under which it flows to a line of strongly coupled N=1 fixed points in the infrared. For these fixed points we find a partial supergravity description.

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