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3d analogs of Argyres-Douglas theories and knot homologies

Fuji, Hiroyuki and Gukov, Sergei and Stošić, Marko and Sułkowski, Piotr (2013) 3d analogs of Argyres-Douglas theories and knot homologies. Journal of High Energy Physics, 2013 (1). Art. No. 175. ISSN 1126-6708. doi:10.1007/JHEP01(2013)175.

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We study singularities of algebraic curves associated with 3d N=2 theories that have at least one global flavor symmetry. Of particular interest is a class of theories T_K labeled by knots, whose partition functions package Poincaré polynomials of the S^r -colored HOMFLY homologies. We derive the defining equation, called the super-A-polynomial, for algebraic curves associated with many new examples of 3d N=2 theories T K and study its singularity structure. In particular, we catalog general types of singularities that presumably exist for all knots and propose their physical interpretation. A computation of super-A-polynomials is based on a derivation of corresponding superpolynomials, which is interesting in its own right and relies solely on a structure of differentials in S^r -colored HOMFLY homologies.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Gukov, Sergei0000-0002-9486-1762
Sułkowski, Piotr0000-0002-6176-6240
Additional Information:© 2013 Published for SISSA by Springer. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: September 18, 2012; Accepted: December 23, 2012; Published: January 29, 2013. We thank M. Aganagic, T. Dimofte, S. Nawata, L. Ng, V. Pestun, and C. Vafa for useful discussions. We also would like to thank the Institute for Theoretical Physics at University of Amsterdam (ITFA), Bethe Center for Theoretical Physics (BCTP) and Physikalisches Institut Universität in Bonn, the Simons Center for Geometry and Physics at Stony Brook, and Mathematical Sciences Center (MSC) of Tsinghua University for hospitality during various stages of this work. The work of H.F. is supported by the Grant-in-Aid for Young Scientists (B) [# 21740179] from the Japan Ministry of Education, Culture, Sports, Science and Technology, and the Grant-in-Aid for Nagoya University Global COE Program, “Quest for Fundamental Principles in the Universe: from Particles to the Solar System and the Cosmos.” The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and in part by NSF Grant PHY-0757647. The work of M.S. is partially supported by Portuguese funds via the FCT - Fundação para a Ciência e a Tecnologia, through project number PTDC/MAT/101503/2008, New Geometry and Topology. M.S. is also partially supported by the Ministry of Science of Serbia, project no. 174012. The research of P.S. is supported by the European Commission under the Marie-Curie International Outgoing Fellowship Programme and the Foundation for Polish Science. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.
Group:Caltech Theory
Funding AgencyGrant Number
Ministry of Education, Culture, Sports, Science and Technology (MEXT)21740179
Nagoya University Global COE ProgramUNSPECIFIED
Department of Energy (DOE)DE-FG03-92-ER40701FG-02
Fundação para a Ciência e a Tecnologia (FCT)PTDC/MAT/101503/2008
Ministry of Science of Serbia174012
Marie Curie International Outgoing FellowshipUNSPECIFIED
Foundation for Polish ScienceUNSPECIFIED
Subject Keywords:Supersymmetric gauge theory; Duality in Gauge Field Theories; ChernSimons Theories; Differential and Algebraic Geometry
Issue or Number:1
Record Number:CaltechAUTHORS:20130405-104147281
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37786
Deposited On:05 Apr 2013 20:51
Last Modified:09 Nov 2021 23:31

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