Michael Bershadsky

D-branes and topological field theories

In the presence of a D-brane a string theory develops a new subsector. We show that for curved D-branes the corresponding sector is a (partially twisted) topological field theory. We use this result to compute the degeneracy of 2-branes wrapped around K3 cycles as well as 3-branes wrapped around CY three-fold vanishing 3-cycles. In both cases we find the degeneracy is in accord with expectation. The counting of BPS states of a gas of 0-branes in the presence of a 4-brane in K3 is considered and it is noted that the effective 0-brane charge is shifted by 1, due to a quantum correction. This is in accord with string duality and the fact that the left-moving ground-state energy of the heterotic string starts at −1. We also show that all the three different topological twistings of four-dimensional N = 4 Yang-Mills theory do arise from curved 3-branes embedded in different spaces (Calabi-Yau manifolds and manifolds with exceptional holonomy groups).

Geometric singularities and enhanced gauge symmetries

Abstract Using “Tates algorithm,” we identify loci in the moduli of F-theory compactifications corresponding to enhanced gauge symmetry. We apply this to test the proposed F-theory/heterotic dualities in six dimensions. We recover the perturbative gauge symmetry enhancements of the heterotic side and the physics of small SO (32) instantons, and discover new mixed perturbative/nonperturbative gauge symmetry enhancements. Upon further toroidal compactification to four dimensions, we derive the chain of Calabi-Yau threefolds dual to various Coulomb branches of heterotic strings.

Holomorphic anomalies in topological field theories

We study the stringy genus-one partition function of N = 2 SCFTs. It is shown how to compute this using an anomaly in decoupling of BRST trivial states from the partition function. A particular limit of this partition function yields the partition function of topological theory coupled to topological gravity. As an application we compute the number of holomorphic elliptic curves over certain Calabi-Yau manifolds including the quintic threefold. This may be viewed as the first application of mirror symmetry at the string quantum level.We study the stringy genus one partition function of

Superstring theory on AdS2 × S2 as a coset supermanifold

N=2

String expansion as large N expansion of gauge theories

SCFTs. It is shown how to compute this using an anomaly in decoupling of BRST trivial states from the partition function. A particular limit of this partition function yields the partition function of topological theory coupled to topological gravity. As an application we compute the number of holomorphic elliptic curves over certain Calabi-Yau manifolds including the quintic threefold. This may be viewed as the first application of mirror symmetry at the string quantum level.

D strings on D manifolds

Instituto de Fisica Teorica Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, Sao Paulo

Large N limit of orbifold field theories

Abstract We consider string perturbative expansion in the presence of D-branes imbedded in orbifolded space-time. In the regime where the string coupling is weak and α ′ → 0, the string perturbative expansion coincides with `t Hoofts large N expansion. We specifically concentrate on theories with d = 4 and N = 0, 1, 2, 4, and use world-sheet orbifold techniques to prove vanishing theorems for the field theory β-functions to all orders in perturbation theory in the large N limit. This is in accord with recent predictions.

ON FOUR-DIMENSIONAL COMPACTIFICATIONS OF F-THEORY

Abstract We study the mechanism for the appearance of massless solitons in type II string compactifications. We find that by combining T -duality with strong/weak duality of type IIB in ten dimensions enhanced gauge symmetries and massless solitonic hypermultiplets encountered in Calabi-Yau compactifications can be studied perturbatively using D -strings (the strong/weak dual to type IIB string) compactified on “ D -manifolds”. In particular the nearly massless solitonic states of the type IIB compactifications correspond to elementary states of D -strings. As examples we consider the D -string description of enhanced gauge symmetries for type IIA string compactification on ALE spaces with A n singularities and type IIB on a class of singular Calabi-Yau 3-folds. The class we study includes as a special case the conifold singularity in which case the perturbative spectrum of the D -string includes the expected massless hypermultiplet with degeneracy one.

Extended N = 2 superconformal structure of gravity and W-gravity coupled to matter

Abstract We consider a certain orbifoldization of the N = 4 field theories that leads to N = 2, 1, 0 field theories in four dimensions. These theories were recently analyzed using the string theory perturbation technique. It was found that in the large N limit all correlation functions of the orbifold theories coincide with those of N = 4, modulo the rescaling of the gauge coupling constant. In this paper we repeat the same analysis using field theoretical language.

PSL(n|n) sigma model as a conformal field theory

Abstract Branches of moduli space of F-theory in four dimensions are investigated. The transition between two branches is described as a 3-brane-instanton transition on a 7-brane. A dual heterotic picture of the transition is presented and the F-theory-heterotic theory map is given. The F-theory data, complex structure of the Calabi-Yau fourfold and the instanton bundle on the 7-brane is mapped to the heterotic bundle on the elliptic Calabi-Yau threefold CY3. The full moduli space has a web structure which is also found in the moduli space of semi-stable bundles on CY3. Matter content of the four-dimensional theory is discussed in both F-theory and heterotic theory descriptions.