Andreas Karch

Branes at Orbifolds versus Hanany Witten in Six Dimensions

We reconstruct non-trivial 6d theories obtained by Blum and Intriligator by considering IIB or SO(32) 5 branes at ALE spaces in the language of Hanany-Witten setups. Using ST duality we make the equivalence of the two approaches manifest, thereby uncovering several new T-duality relations between the group theoretic data describing the embedding of the instantonic 5 brane in the ALE and brane positions in the Hanany-Witten language. We construct several new 6d theories, which can be understood as arising on 5 branes in IIB orientifolds with oppositely charged orientifold planes recently introduced by Witten.

Equivalence of geometric engineering and Hanany-Witten via fractional branes

Abstract We present an explicit relation between the Hanany-Witten and Geometric Engineering approaches of realizing gauge theories in string theory. The last piece in the puzzle is a T -duality relating arbitrary Hanany-Witten setups and fractional branes.

MATRIX DESCRIPTION OF M-THEORY ON T6

Abstract We give some evidence that the worldvolume theory of the M-theory KK 6-brane is governed by a non-critical membrane theory. We use this theory to give a matrix description of M-theory on T 6 .

Brane dynamics and chiral non-chiral transitions

Abstract We study brane realizations of chiral matter in N = 1 supersymmetric gauge theories in four dimensions. A “cross” configuration which leads to “flavor doubling” is found to have a superpotential. The main example is realized using a special “fork” configuration. Many of the results are found by studying a SU × SU product gauge group first. The chiral theory is then an orientifold projection of the product gauge group. An interesting observation in the brane picture is that there are transitions between chiral and non-chiral models. These transitions are closely related to small instanton transitions in six dimensions.

Branes and six dimensional fixed points

We analyze brane configurations corresponding to non-trivial six dimensional fixed points. Several results previously obtained from a pure field theoretical analysis are rederived in the brane language.

Seiberg duality in three dimensions

We analyze three dimensional gauge theories with Sp gauge group. We find that in some regime the theory should be described in terms of a dual theory, very much in the spirit of Seiberg duality in four dimensions. This duality does not coincide with mirror symmetry.

INFRARED BEHAVIOUR OF SOFTLY BROKEN SQCD AND ITS DUAL

Abstract Applying the recently obtained results on the renormalization of soft supersymmetry-breaking parameters, we investigate the infrared behaviour of the softly broken supersymmetric QCD as well as its dual theory in the conformal window. Under general assumptions on β -functions, it is shown that the soft supersymmetry-breaking parameters asymptotically vanish in the infrared limit so that superconformal symmetry in softly broken supersymmetric QCD and in its dual theory revives at the infrared fixed point, provided the soft scalar masses satisfy certain renormalization group invariant relations. If these relations are not satisfied, there exist marginal operators in both theories that lead to the breaking of supersymmetry and also colour symmetry.

Field Theory Dynamics from branes in String Theory

I review certain aspects of Hanany-Witten setups and other approaches used to embed (and solve) gauge theories in string theory. Applications covered include dualities in 4 and 3 dimensions, fixed points in 6 dimensions, phase transitions between different geometric backgrounds and dualities between branes and geometry.

More on N = 1 self-dualities and exceptional gauge groups

Abstract Starting from a generalization of a recent result on self-duality [C. Csaki, M. Schmaltz, W. Skiba and J. Terning, hep-th/9701191], 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.

DUALITIES IN ALL-ORDER FINITE N = 1 GAUGE THEORIES

Abstract We search for dual gauge theories of all-loop finite, N = 1 supersymmetric gauge theories. It is shown how to find explicitly the dual gauge theories of almost all chiral, N = 1, all-loop finite gauge theories, while several models have been discussed in detail, including a realistic finite SU (5) unified theory. Out of our search only one all-loop, N = 1 finite SO (10) theory emerges, so far, as a candidate for exhibiting also S -duality.