Amihay Hanany

Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics

We propose an explanation via string theory of the correspondence between the Coulomb branch of certain three-dimensional supersymmetric gauge theories and certain moduli spaces of magnetic monopoles. The same construction also gives an explanation, via SL(2, Z) duality of Type IIB superstrings, of the recently discovered “mirror symmetry” in three dimensions. New phase transitions in three dimensions as well as new infrared fixed points and even new coupling constants not present in the known Lagrangians are predicted from the string theory construction. An important role in the construction is played by a novel aspect of brane dynamics in which a third brane is created when two branes cross.

Aspects of N = 2 supersymmetric gauge theories in three dimensions

Abstract We consider general aspects of N = 2 gauge theories in three dimensions, including their multiplet structure, anomalies and non-renormalization theorems. For U (1) gauge theories, we discuss the quantum corrections to the moduli space, and their relation to “mirror symmetries” of 3d N = 4 theories. Mirror symmetry is given an interpretation in terms of vortices. For SU ( N c ) gauge groups with N f fundamental flavors, we show that, depending on the number of flavors, there are quantum moduli spaces of vacua with various phenomena near the origin.

Gauge theories from toric geometry and brane tilings

We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3-branes probing a toric Calabi-Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki-Einstein manifolds La,b,c is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform a-maximisation as well as Z-minimisation to compute the exact R-charges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily La,b,a, whose smallest member is the Suspended Pinch Point.

Webs of (p,q) 5-branes, five dimensional field theories and grid diagrams

We continue to study 5d N = 1 supersymmetric field theories and their compactifications on a circle through brane configurations. We develop a model, which we call (p,q) Webs, which enables simple geometrical computations to reproduce the known results, and facilitates further study. The physical concepts of field theory are transparent in this picture, offering an interpretation for global symmetries, local symmetries, the effective (running) coupling, the Coulomb and Higgs branches, the monopole tensions, and the mass of BPS particles. A rule for the dimension of the Coulomb branch is found by introducing Grid Diagrams. Some known classifications of field theories are reproduced. In addition to the study of the vacuum manifold we develop methods to determine the BPS spectrum. Some states, such as quarks, correspond to instantons inside the 5-brane which we call strips. In general, these may not be identified with (p,q) strings. We describe how a strip can bend out of a 5-brane, becoming a string. A general BPS state corresponds to a Web of strings and strips. For special values of the string coupling a few strips can combine and leave the 5-brane as a string.

An infinite family of superconformal quiver gauge theories with Sasaki-Einstein duals.

We describe an infinite family of quiver gauge theories that are AdS/CFT dual to a corresponding class of explicit horizon Sasaki-Einstein manifolds. The quivers may be obtained from a family of orbifold theories by a simple iterative procedure. A key aspect in their construction relies on the global symmetry which is dual to the isometry of the manifolds. For an arbitrary such quiver we compute the exact R-charges of the fields in the IR by applying a-maximization. The values we obtain are generically quadratic irrational numbers and agree perfectly with the central charges and baryon charges computed from the family of metrics using the AdS/CFT correspondence. These results open the way for a systematic study of the quiver gauge theories and their dual geometries.

D-brane gauge theories from toric singularities and toric duality

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Branes, superpotentials and superconformal fixed points

Abstract We analyze various brane configurations corresponding to field theories in three, four and five dimensions. We find brane configurations which correspond to three-dimensional N = 2 and four-dimensional N = 1 supersymmetric QCD theories with quartic superpotentials, in which what appear to be “hidden parameters” play an important role. We discuss the construction of five-dimensional N = 1 supersymmetric gauge theories and superconformal fixed points using branes, which leads to new five-dimensional N = 1 superconformal field theories. The same five-dimensional theories are also used, in a surprising way, to describe new superconformal fixed points of three-dimensional N = 2 supersymmetric theories, which have both “electric” and “magnetic” Coulomb branches.

Small E8 instantons and tensionless non-critical strings

T-duality is used to extract information on an instanton of zero size in the E8 × E8 heterotic string. We discuss the possibility of the appearance of a tensionless anti-self-dual non-critical string through an implementation of the mechanism suggested by Strominger of two coincident 5-branes. It is argued that when an instanton shrinks to zero size a tensionless non-critical string appears at the core of the instanton. It is further conjectured that the appearance of tensionless strings in the spectrum leads to new phase transitions in six dimensions in much the same way as massless particles do in four dimensions.

Quivers, tilings, branes and rhombi

We describe a simple algorithm that computes the recently discovered brane tilings for a given generic toric singular Calabi-Yau threefold. This therefore gives AdS/CFT dual quiver gauge theories for D3-branes probing the given non-compact manifold [1]. The algorithm solves a longstanding problem by computing superpotentials for these theories directly from the toric diagram of the singularity. We study the parameter space of a-maximization; this study is made possible by identifying the R-charges of bifundamental fields as angles in the brane tiling. We also study Seiberg duality from a new perspective.

Tilings, Chern-Simons theories and M2 branes

A new infinite class of Chern-Simons theories in 2+1 dimensions is presented using brane tilings. The new class reproduces all known cases so far and introduces many new models that are dual to M2 brane theories which probe a toric non-compact singular CY 4-fold. The master space of the quiver theory is used as a tool to construct the moduli space for this class and the Hilbert Series is computed for a selected set of examples.