The dual superconformal theory forL^p,q,rmanifolds

Abstract

We present the superconformal gauge theory living on the world-volume of D3 branes probing the toric singularities with horizon the recently discovered Sasaki-Einstein manifolds L p,q,r . Various checks of the identification are made by comparing the central charge and the R-charges of the chiral fields with the information that can be extracted from toric geometry. Fractional branes are also introduced and the physics of the associated duality cascade discussed.agostino.

Integrability on the master space

“…Every endpoint of each arrow ends on a node, and the only admissible representation are adjoint and bifundamental. For instance in the case of dP 0 the quiver is given in the Figure 1 and it is associated to a product of three SU (N ) gauge groups with three chiral bifundamental fields connecting each pair of nodes, X (i) 12 , X (i) 23 and X (i) 31 , with i = 1, 2, 3. Useful tools to describe the quiver are the oriented incidence and the adjacency matrices.…”

Dimers and orientifolds

“…This recipe, which generalizes [2] for orientifold singularities, is very involved in practice, and only a few simple cases have been worked out in [52]. For a class of toric singularities (known as L aba theories in modern terminology [35,20,23]), it is possible to perform a T-duality [54,55] to a Hanany-Witten (HW) setup [16] and introduce orientifold planes [56 -58]. Using such tools, several classes of orientifolds of C 2 /Z N ×C were constructed in [59] and recovered using CFT tools.…”

“…28 These are in the L abc family for which explicit metrics are known [109,110]. Probing a real cone over L aba spaces with D3-branes gives interesting gauge theories [35,20,23]. The T-dual theory is an elliptic model, i.e.…”

“…These are chains of bi-fundamental fields which correspond to fundamental cells of the dimer or respectively of the shiver. 23 S-chains. A S-chain is constructed in the following way: Take an arbitrary bifundamental field contained in a monomial of the superpotential as the first field in the S-chain.…”

“…Then jump to the unique other monomial containing this field. 24 Take the right field of it as the next one 23 In fact, the fields need not necessarily be bi-fundamentals. For example, adjoint fields may occur in the superpotential as well.…”