Duality cascades and duality walls

We recast the phenomenon of duality cascades in terms of the Cartan matrix associated to the quiver gauge theories appearing in the cascade. In this language, Seiberg dualities for the different gauge factors correspond to Weyl reflections. We argue that the UV behavior of different duality cascades depends markedly on whether the Cartan matrix is affine ADE or not. In particular, we find examples of duality cascades that can't be continued after a finite energy scale, reaching a "duality wall", in terminology due to M. Strassler. For these duality cascades, we suggest the existence of a UV completion in terms of a little string theory.Comment: harvmac, 24 pages, 4 figures. v2: references added. v3: reference adde

Gale duality and Koszul duality

Given an affine hyperplane arrangement with some additional structure, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul dual to each other, and that the roles of the two algebras are reversed by Gale duality. We also study the centers and representation categories of our algebras, which are in many ways analogous to integral blocks of category O.Comment: 55 pages; v2 contains significant revisions to proofs and to some of the results. Section 7 has been deleted; that material will be incorporated into a later paper by the same author

Self-duality of the D1-D5 near-horizon

We explore fermionic T-duality and self-duality in the geometry AdS3 x S3 x T4 in type IIB supergravity. We explicitly construct the Killing spinors and the fermionic T-duality isometries and show that the geometry is self-dual under a combination of two bosonic AdS3 T-dualities, four fermionic T-dualities and either two additional T-dualities along T4 or two T-dualities along S3. In addition, we show that the presence of a B-field acts as an obstacle to self-duality, a property attributable to S- duality and fermionic T-duality not commuting. Finally, we argue that fermionic T-duality may be extended to CY2 = K3, a setting where we cannot explicitly construct the Killing spinors.Comment: 24 pages, references added, changes made to reinforce the point that S-duality and fermionic T-duality generically do not commute, version accepted to JHE

Toric Duality Is Seiberg Duality

We study four N=1 SU(N)^6 gauge theories, with bi-fundamental chiral matter and a superpotential. In the infrared, these gauge theories all realize the low-energy world-volume description of N coincident D3-branes transverse to the complex cone over a del Pezzo surface dP_3 which is the blowup of P^2 at three generic points. Therefore, the four gauge theories are expected to fall into the same universality class--an example of a phenomenon that has been termed "toric duality." However, little independent evidence has been given that such theories are infrared-equivalent. In fact, we show that the four gauge theories are related by the N=1 duality of Seiberg, vindicating this expectation. We also study holographic aspects of these gauge theories. In particular we relate the spectrum of chiral operators in the gauge theories to wrapped D3-brane states in the AdS dual description. We finally demonstrate that the other known examples of toric duality are related by N=1 duality, a fact which we conjecture holds generally.Comment: 46 pages, 2 figures, harvma