Quantum effective action, wave functions, and Yang-Mills theory in (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>) dimensions

Nair, V. P.

doi:10.1103/physrevd.85.105019

Cited by 6 publications

(2 citation statements)

References 32 publications

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“…It is possible to include edge modes on the boundary of the full space as well, although they are not important for the entanglement entropy. The Hamiltonian for the full space has a form similar to (20) (without the subscript I, of course). The term involving E is the term corresponding to the edge modes.…”

Section: The Maxwell Theorymentioning

confidence: 99%

Gauge-invariant variables and entanglement entropy

2017

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The entanglement entropy (EE) of gauge theories in three spacetime dimensions is analyzed using manifestly gauge-invariant variables defined directly in the continuum. Specifically, we focus on the Maxwell, Maxwell-Chern-Simons (MCS), and nonabelian Yang-Mills theories. Special attention is paid to the analysis of edge modes and their contribution to EE. The contact term is derived without invoking the replica method and its physical origin is traced to the phase space volume measure for the edge modes. The topological contribution to the EE for the MCS case is calculated. For all the abelian cases, the EE presented in this paper agrees with known results in the literature. The EE for the nonabelian theory is computed in a gauge-invariant gaussian approximation, which incoprorates the dynamically generated mass gap. A formulation of the contact term for the nonabelian case is also presented.

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Section: The Maxwell Theorymentioning

confidence: 99%

Gauge-invariant variables and entanglement entropy

2017

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“…I thank the organizers for inviting me to this very interesting workshop and for accommodating my difficult schedule. After this talk was presented at the workshop, some of the work has been written up as a research article [12]; it contains some more details and derivations.…”

Section: What Can We Say About Excited States?mentioning

confidence: 99%

Gauge invariant mass terms and wave functions

Nair¹

2012

Proceedings of International Workshop on QCD Green's Functions, Confinement and Phenomenology — PoS(QCD-TNT-II)

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We outline a method of relating the quantum effective action and the ground state wave function of a field theory. This method, along with a gauge-invariant mass term and the previously obtained vacuum wave function, is used to arrive at the leading terms of the 3d-covariant quantum effective action for the Yang-Mills theory in three (or 2+1) dimensions. Some features of this effective action are also discussed.

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A geometric approach to the Yang-Mills mass gap

Mondal

2023

J. High Energ. Phys.

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I provide a new idea based on geometric analysis to obtain a positive mass gap in pure non-abelian renormalizable Yang-Mills theory. The orbit space, that is the space of connections of Yang-Mills theory modulo gauge transformations, is equipped with a Riemannian metric that naturally arises from the kinetic part of reduced classical action and admits a positive definite sectional curvature. The corresponding regularized Bakry-Émery Ricci curvature (if positive) is shown to produce a mass gap for 2+1 and 3+1 dimensional Yang-Mills theory assuming the existence of a quantized Yang-Mills theory on (ℝ1+2, η) and (ℝ1+3, η), respectively. My result on the gap calculation, described at least as a heuristic one, applies to non-abelian Yang-Mills theory with any compact semi-simple Lie group in the aforementioned dimensions. In 2+1 dimensions, the square of the Yang-Mils coupling constant $$ {g}_{YM}^2 $$ g YM 2 has the dimension of mass, and therefore the spectral gap of the Hamiltonian is essentially proportional to $$ {g}_{YM}^2 $$ g YM 2 with proportionality constant being purely numerical as expected. Due to the dimensional restriction on 3+1 dimensional Yang-Mills theory, it seems one ought to introduce a length scale to obtain an energy scale. It turns out that a certain ‘trace’ operation on the infinite-dimensional geometry naturally introduces a length scale that has to be fixed by measuring the energy of the lowest glu-ball state. However, this remains to be understood in a rigorous way.

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Quantum effective action, wave functions, and Yang-Mills theory in (2+1) dimensions

Cited by 6 publications

References 32 publications

Gauge-invariant variables and entanglement entropy

Gauge-invariant variables and entanglement entropy

Gauge invariant mass terms and wave functions

A geometric approach to the Yang-Mills mass gap

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