3d Partition Function as Overlap of Wavefunctions

We study moduli spaces of a class of three dimensional N = 4 gauge theories which are in one-to-one correspondence with a certain set of ordered pairs of integer partitions. It was found that these theories can be realised on brane intervals in Type IIB string theory and can therefore be described using linear quiver diagrams. Mirror symmetry was known to act on such a theory by exchanging the partitions in the corresponding ordered pair, and hence the quiver diagram of the mirror theory can be written down in a straightforward way. The infrared Coulomb branch of each theory can be studied using moment map equations for a hyperKähler quotient of the Higgs branch of the mirror theory. We focus on three infinite subclasses of these singular hyperKähler spaces which are complete intersections. The Hilbert series of these spaces are computed in order to count generators and relations, and they turn out to be related to the corresponding partitions of the theories. For each theory, we explicitly discuss the generators of such a space and relations they satisfy in detail. These relations are precisely the defining equations of the corresponding complete intersection space. arXiv:1110.6203v2 [hep-th]

“…This is in agreement with the known property by mirror symmetry that the Higgs and Coulomb branches are identical (see, e.g. [1,4,5]).…”

supporting

confidence: 91%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Complete intersection moduli spaces in $ \mathcal{N} = 4 $ gauge theories in three dimensions

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Yamazaki

2012

Self Cite

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We study 4d superconformal indices for a large class of N = 1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T2 . An exchange of loops, which we call a "double YangBaxter move", gives the Seiberg duality of the gauge theory, and the invariance of the index under the duality is translated into the Yang-Baxter-type equation of a spin system defined on a "Z-invariant" lattice on T 2 . When we compactify the gauge theory to 3d, Higgs the theory and then compactify further to 2d, the superconformal index reduces to an integral of quantum/classical dilogarithm functions. The saddle point of this integral unexpectedly reproduces the hyperbolic volume of a hyperbolic 3-manifold. The 3-manifold is obtained by gluing hyperbolic ideal polyhedra in H 3 , each of which could be thought of as a 3d lift of the faces of the 2d bipartite graph. The same quantity is also related with the thermodynamic limit of the BPS partition function, or equivalently the genus 0 topological string partition function, on a toric Calabi-Yau manifold dual to quiver gauge theories. We also comment on brane realization of our theories. This paper is a companion to another paper summarizing the results [1].

4D and 2D superconformal index with surface operator

Nakayama

2011

We study the superconformal index of the N=4 super-Yang-Milles theory on S^3 X S^1 with the half BPS superconformal surface operator (defect) inserted at the great circle of S^3. The half BPS superconformal surface operators preserve the same supersymmetry as well as the symmetry of the chemical potential used in the definition of the superconformal index, so the structure and the parameterization of the superconformal index remain unaffected by the presence of the surface operator. On the surface defect, a two-dimensional (4,4) superconformal field theory resides, and the four-dimensional superconformal index may be regarded as a superconformal index of the two-dimensional (4,4) superconformal field theory coupled with the four-dimensional bulk system. We construct the matrix model that computes the superconformal index with the surface operator when it couples with the bulk N=4 super-Yang-Milles theory through the defect hypermultiplets on it.Comment: 22 pages, v3: typos corrected and references adde