On Framed Quivers, BPS Invariants and Defects
Confluentes Mathematici, Volume 9 (2017) no. 2, pp. 71-99.

In this note we review some of the uses of framed quivers to study BPS invariants of Donaldson-Thomas type. We will mostly focus on non-compact Calabi-Yau threefolds. In certain cases the study of these invariants can be approached as a generalized instanton problem in a six dimensional cohomological Yang-Mills theory. One can construct a quantum mechanics model based on a certain framed quiver which locally describes the theory around a generalized instanton solution. The problem is then reduced to the study of the moduli spaces of representations of these quivers. Examples include the affine space and noncommutative crepant resolutions of orbifold singularities. In the second part of the survey we introduce the concepts of defects in physics and argue with a few examples that they give rise to a modified Donaldson-Thomas problem. We mostly focus on divisor defects in six dimensional Yang-Mills theory and their relation with the moduli spaces of parabolic sheaves. In certain cases also this problem can be reformulated in terms of framed quivers.

Published online:
DOI: 10.5802/cml.42
Classification: 14N35, 81T13, 81T60
Keywords: Donaldson-Thomas theory, BPS invariants, Quivers and Representation Theory, Defects in Quantum Field Theory
Michele Cirafici 1

1 Center for Mathematical Analysis, Geometry and Dynamical Systems Mathematics Department; Instituto Superior Técnico, Universidade de Lisboa Av. Rovisco Pais, 1049-001 Lisboa, Portugal
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Michele Cirafici. On Framed Quivers, BPS Invariants and Defects. Confluentes Mathematici, Volume 9 (2017) no. 2, pp. 71-99. doi : 10.5802/cml.42. https://cml.centre-mersenne.org/articles/10.5802/cml.42/

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