2020/03/31 by Shai M. Chester, Silviu S. Pufu · 1 citation
Physics and Astronomy · #Correlation function (quantum field theory) #Coupling (piping) #Coupling constant #Gauge (firearms) #Gauge theory #Limit (mathematics) #Multiplet #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Quantum and Classical Electrodynamics #Superstring theory #Supersymmetric gauge theory #Supersymmetry #hep-th
paper · pdf · doi:10.1007/jhep01(2021)103
25 pages plus appendices, v2 submitted to JHEP, minor typos fixed
openalex created_date 2020/03/23 · arxiv created 2020/08/12 · openalex publication_date 2021/01/19 · arxiv updated 2021/02/03 · openalex updated_date 2026/08/06
A bstract When the SU( N ) N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 super-Yang-Mills (SYM) theory with complexified gauge coupling τ is placed on a round four-sphere and deformed by an N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2-preserving mass parameter m , its free energy F ( m, τ, τ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>τ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> ) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative ∂m4F(m,τ, τ)|m=0. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>∂</mml:mi> <mml:mi>m</mml:mi> <mml:mn>4</mml:mn> </mml:msubsup> <mml:mi>F</mml:mi> <mml:mfenced> <mml:mi>m</mml:mi> <mml:mi>τ</mml:mi> <mml:mover> <mml:mi>τ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mfenced> <mml:mfenced> <mml:msub> <mml:msub> <mml:mrow/> <mml:mi>m</mml:mi> </mml:msub> <mml:mrow> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mfenced> </mml:math> of the sphere free energy and the integrated stress-tensor multiplet four-point function in the N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative ∂τ ∂_τ∂m2F(m,τ, τ)|m=0. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>∂</mml:mi> <mml:mi>τ</mml:mi> </mml:msub> <mml:msub> <mml:mi>∂</mml:mi> <mml:mover> <mml:mi>τ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:msub> <mml:msubsup> <mml:mi>∂</mml:mi> <mml:mi>m</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mi>F</mml:mi> <mml:mfenced> <mml:mi>m</mml:mi> <mml:mi>τ</mml:mi> <mml:mover> <mml:mi>τ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mfenced> <mml:mfenced> <mml:msub> <mml:msub> <mml:mrow/> <mml:mi>m</mml:mi> </mml:msub> <mml:mrow> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mfenced> </mml:math> , and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large N and large ’t Hooft coupling λ expansion of the N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM correlator at separated points. In particular, we determine the leading large- λ term in the N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM correlation function at order 1 /N 8 . This is three orders beyond the planar limit.