Universität zu Köln

Banerjee, Sibasish ORCID: 0000-0003-1348-3550, Longhi, Pietro ORCID: 0000-0002-5558-0386 and Romo, Mauricio (2023). A-branes, Foliations and Localization. Ann. Henri Poincare, 24 (4). S. 1077 - 1137. CHAM: SPRINGER INT PUBL AG. ISSN 1424-0661

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Abstract

This paper studies a notion of enumerative invariants for stable A-branes and discusses its relation to invariants defined by spectral and exponential networks. A natural definition of stable A-branes and their counts is provided by the string theoretic origin of the topological A-model. This is the Witten index of the supersymmetric quantum mechanics of a single D3 brane supported on a special Lagrangian in a Calabi-Yau threefold. Geometrically, this is closely related to the Euler characteristic of the A-brane moduli space. Using the natural torus action on this moduli space, we reduce the computation of its Euler characteristic to a count of fixed points via equivariant localization. Studying the A-branes that correspond to fixed points, we make contact with definitions of spectral and exponential networks. We find agreement between the counts defined via the Witten index, and the BPS invariants defined by networks. By extension, our definition also matches with Donaldson-Thomas invariants of B-branes related by homological mirror symmetry.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Banerjee, Sibasish UNSPECIFIED orcid.org/0000-0003-1348-3550 UNSPECIFIED Longhi, Pietro UNSPECIFIED orcid.org/0000-0002-5558-0386 UNSPECIFIED Romo, Mauricio UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-679593
DOI:	10.1007/s00023-022-01231-8
Journal or Publication Title:	Ann. Henri Poincare
Volume:	24
Number:	4
Page Range:	S. 1077 - 1137
Date:	2023
Publisher:	SPRINGER INT PUBL AG
Place of Publication:	CHAM
ISSN:	1424-0661
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MIRROR SYMMETRY; SPECTRAL NETWORKS; SUPERSYMMETRY; CONSTRUCTION; COHOMOLOGY; DUALITY; STRINGS; STATES Multiple languages Physics, Multidisciplinary; Physics, Particles & Fields; Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67959