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3d expansions of 5d instanton partition functions

2017/11/30 by Fabrizio Nieri, Yiwen Pan, Maxim Zabzine
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Gauge theory #Instanton #Intersection (aeronautics) #Linear subspace #Particle physics theoretical and experimental studies #Partition (number theory) #Partition function (quantum field theory) #Quantum Chromodynamics and Particle Interactions #Supersymmetric gauge theory #Unitary state #hep-th #math.QA

paper · pdf · doi:10.1007/jhep04(2018)092

v1: 30 pages. v2: references added. v3:JHEP version with added references and clarifications

openalex created_date 2017/12/04 · openalex publication_date 2018/04/01 · arxiv created 2018/04/13 · arxiv updated 2018/05/09 · openalex updated_date 2026/08/05

Abstract

A bstract We propose a set of novel expansions of Nekrasov’s instanton partition functions. Focusing on 5d supersymmetric pure Yang-Mills theory with unitary gauge group on ℂ_q,t-12× \mathbbS1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>ℂ</mml:mi> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>,</mml:mo> <mml:msup> <mml:mi>t</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> , we show that the instanton partition function admits expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces ℂq× \mathbbS1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℂ</mml:mi> <mml:mi>q</mml:mi> </mml:msub> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> , ℂt-1× \mathbbS1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℂ</mml:mi> <mml:msup> <mml:mi>t</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:msub> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> and their intersection along \mathbbS1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> . These new expansions are natural from the BPS/CFT viewpoint, as they can be matched with W q,t correlators involving an arbitrary number of screening charges of two kinds. Our constructions generalize and interpolate existing results in the literature.

Citations