Related papers: Exact Results in Quiver Quantum Mechanics and BPS …
We show that the supersymmetric partition function of three-dimensional N=2 R-symmetric Chern-Simons-matter theories on the squashed S^3 and on S^2 x S^1 can be computed with the so-called Higgs branch localization method, alternative to…
We study half-BPS surface operators in supersymmetric gauge theories in four and five dimensions following two different approaches. In the first approach we analyze the chiral ring equations for certain quiver theories in two and three…
In this work, we first solve complex Morse flow equations for the simplest case of a bosonic harmonic oscillator to discuss localization in the context of Picard-Lefschetz theory. We briefly touch on the exact non-BPS solutions of the…
We show that two elementary worldline path integrals-the thermal partition function of the harmonic oscillator and the one-loop effective action of scalar QED in a constant field strength-exhibit a natural form of supersymmetric…
In quiver quantum mechanics with 4 supercharges, supersymmetric ground states are known to be in one-to-one correspondence with Dolbeault cohomology classes on the moduli space of stable quiver representations. Using supersymmetric…
In study of four-dimensional BPS states, quiver quantum mechanics plays a central role. The Coulomb phases capture the multi-centered nature of such states, and are well understood in the context of wall-crossing. The Higgs phases are given…
We review the problem of BPS state counting described by the generalized quiver matrix model of ADHM type. In four dimensions the generating function of the counting gives the Nekrasov partition function and we obtain generalization in…
We study N = 4 quiver theories on the three-sphere. We compute partition functions using the localisation method by Kapustin et al. solving exactly the matrix integrals at finite N, as functions of mass and Fayet-Iliopoulos parameters. We…
In previous work we have shown that the equivariant index of multi-centered N=2 black holes localizes on collinear configurations along a fixed axis. Here we provide a general algorithm for enumerating such collinear configurations and…
For D=4 BPS state construction, counting, and wall-crossing thereof, quiver quantum mechanics offers two alternative approaches, the Coulomb phase and the Higgs phase, which sometimes produce inequivalent counting. The authors have…
We consider 4d $\mathcal{N}=1$ gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry…
We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…
Equivariant localization theory is a powerful tool that has been extensively used in the past thirty years to elegantly obtain exact integration formulas, in both mathematics and physics. These integration formulas are proved within the…
We study the partition functions of topologically twisted 3d $\mathcal{N}=2$ gauge theories on a hemisphere spacetime with boundary $HS^2 \times S^1$. We show that the partition function may be localised to either the Higgs branch or the…
We derive a localization formula for the refined index of gauged quantum mechanics with four supercharges. Our answer takes the form of a residue integral on the complexified Cartan subalgebra of the gauge group. The formula captures the…
Two pictures of BPS bound states in Calabi-Yau compactifications of type II string theory exist, one as a set of particles at equilibrium separations from each other, the other as a fusion of D-branes at a single point of space. We show how…
We give a path integral construction of the quantum mechanical partition function for gauged finite groups. Our construction gives the quantization of a system of $d$, $N\times N$ matrices invariant under the adjoint action of the symmetric…
We study four-dimensional $\mathcal N=2$ superconformal circular, cyclic symmetric quiver theories which are planar equivalent to $\mathcal N=4$ super Yang-Mills. We use localization to compute nonplanar corrections to the free energy and…
We discuss localization of the path integral for supersymmetric gauge theories with an R-symmetry on Hermitian four-manifolds. After presenting the localization locus equations for the general case, we focus on backgrounds with S^1 x S^3…
We discuss a general procedure to obtain 1/2 BPS partition functions for generic N=1 quiver gauge theories. These functions count the gauge invariant operators (bosonic and fermionic), charged under all the global symmetries (mesonic and…