Witten index and wall crossing

By K. Hori, Hee-Cheol Kim, Piljin Yi. 2014

179 citations recorded by the source corpus.

A bstractWe compute the Witten index of one-dimensional gauged linear sigma models with at least N$$ \mathcal{N} $$ = 2 supersymmetry. In the phase where the gauge group is broken to a finite group, the index is expressed as a certain residue integral. It is subject to a change as the Fayet-Iliopoulos parameter is varied through the phase boundaries. The wall crossing formula is expressed as an integral at infinity of the Coulomb branch. The result is applied to many examples, including quiver quantum mechanics that is relevant for BPS states in d = 4 N$$ \mathcal{N} $$ =2 theories.

Subfields: Condensed Matter Physics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/43b1573b01464ef2b0a3331ec28aa81d64c4ddec

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In Condensed Matter Physics

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Citations in the corpus

Comments on twisted indices in 3d supersymmetric gauge theories (2016, methodology): “This is essentially the same the discussion in the previous literatures [7, 8].”
Black hole microstates in AdS4 from supersymmetric localization (2015, background): “In quantum mechanics we should add a Wilson line [61].”
Supersymmetric partition functions on Riemann surfaces (2016, methodology): “In doing the computation, one encounters a system of bosonic and fermionic zero-modes that can be dealt with using the method in [6, 7] (see also [3, 5, 24, 25]), originally envisaged to compute the elliptic genus of two-dimensional gauge theories.”
General instanton counting and 5d SCFT (2014, background): “3 on the general index have an overlap with [39].”
Schur indices, BPS particles, and Argyres-Douglas theories (2015, methodology): “[44, 45] for a systematic calculation for both the gauge theory and Argyres-Douglas examples.”
A topologically twisted index for three-dimensional supersymmetric theories (2015, methodology): “We do not repeat all the steps of the argument, which has been spelled out in details in [4, 5] and [6], but we simply review the logic and mention the necessary modifications to deal with the boundary components.”
Defects and quantum Seiberg-Witten geometry (2014, unknown): “See [51, 58, 59] for more detailed explanations.”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “4) can itself be interpreted as the flavored Witten index [16] of a one-dimensional theory obtained in the q → 0 limit, corresponding to sending the size of M3 to zero.”