David Kutasov

Branes and N = 1 duality in string theory

Abstract We propose a construction of dual pairs in four dimensional N = 1 supersymmetric Yang-Mills theory using branes in type IIA string theory.

Brane dynamics and N=1 supersymmetric gauge theory

Abstract We discuss some aspects of the relation between space-time properties of branes in string theory, and the gauge theory on their world-volume, for models invariant under four supercharges in three and four dimensions. We show that a simple set of rules governing brane dynamics reproduces many features of gauge theory. We study theories with U ( N c ), SO ( N c ), and Sp ( N c ) gauge groups and matter in the fundamental and two-index tensor representations, and use the brane description to establish Seibergs electric-magnetic duality for these models.

Geometry on the space of conformal field theories and contact terms

Abstract Some aspects of the geometry on the moduli space of CFT are discussed. The two-point function of the moduli is the metric on the space, the connection appears as a contact term and the four-point function determines the Riemann tensor. The relation between the OPE of moduli and the curvature is examined, and a condition for homogeneity is obtained.

M-branes and N = 2 strings

The string field theory of N = (2,1) heterotic strings describes a set of self-dual Yang - Mills fields coupled to self-dual gravity in 2 + 2 dimensions. We show that the exact classical action for this field theory is a certain complexification of the Green - Schwarz/Dirac - Born - Infeld string action, closely related to the four-dimensional Wess - Zumino action describing self-dual gauge fields. This action describes the world-volume of a (2 + 2)D `M-brane, which gives rise upon different null reductions to critical strings and membranes. We discuss a number of further properties of N = 2 heterotic strings, such as the geometry of null reduction, general features of a covariant formulation, and possible relations to BPS and GKM algebras.

String theory and the non-abelian thirring model

Abstract The β function of the non-abelian Thirring model is shown to be negative for all values of the coupling for which the model is unitary. An explicit expression for β and the effective potential is obtained to leading order in 1 k . Possible relevance to string theory is briefly discussed.

Constraining de Sitter Space in String Theory

We argue that the heterotic string does not have classical vacua corresponding to de Sitter space-times of dimension four or higher. The same conclusion applies to type II vacua in the absence of Ramond-Ramond fluxes. Our argument extends prior supergravity no-go results to regimes of high curvature. We discuss the interpretation of the heterotic result from the perspective of dual type II orientifold constructions. Our result suggests that the genericity arguments used in string landscape discussions should be viewed with caution.

Duality off the critical point in two-dimensional systems with non abelian symmetries

Abstract A duality transformation of a non abelian Thirring model with coupling constant λ and level k to one with coupling 1/λ and level (−k−2Q) is derived. At λ=1 the theory acquires two dimensional gauge invariance, which freezes the current degrees of freedom. This point is infinitely far away from the origin in field space. It serves as a boundary between disconnected regions in this space. In string theory a similar mechanism appears to lead to the existence of maximum allowed background fields.

Modular invariance, chiral anomalies and contact terms

Abstract The chiral anomaly in heterotic strings with full and partial modular invariance in D = 2n + 2 dimensions is calculated. The boundary terms which were present in previous calculations are shown to be cancelled in the modular-invariant case by contact terms, which can be obtained by an appropriate analytic continuation. The relation to the low-energy field theory is explained. In theories with partial modular invariance, an expression for the anomaly iis obtained and shown to be non-zero in general.

New Directions in Quantum Field Theory

I briefly review some of the new insights into the dynamics of supersymmetric gauge theories in different dimensions that were obtained recently by realizing them as low energy theories on branes.

The algebraic structure of the fermionic string

Abstract The local structure of the product expansion algebra of the covariant NSR string is analyzed. An “on-shell” Kac-Moody like algebra is found to generate the BRST invariant part of the covariant lattice Γ 5,1 . This algebra is a local version of ten-dimensional SUSY.