$T\overline{T}$-deformation of $q$-Yang-Mills theory

Leonardo Santilli; Miguel Tierz; Richard J. Szabo

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$T\overline{T}$-deformation of $q$-Yang-Mills theory

Leonardo Santilli, Richard J. Szabo, Miguel Tierz

High Energy Physics - Theory · Submitted 1 Sep 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that the $T\overline{T}$-deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large $N$ factorization into chiral and anti-chiral sectors.

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We derive the $T\overline{T}$-perturbed version of two-dimensional $q$-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the $T\overline{T}$-deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large $N$ factorization into chiral and anti-chiral sectors. For the $U(N)$ gauge theory on the sphere, we show that the large $N$ phase transition persists, and that it is of third order and induced by instantons. The effect of the $T\overline{T}$-deformation is to decrease the critical value of the 't Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for $(q,t)$-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large $N$ limit of Yang-Mills theory, showing that the $T\overline{T}$-deformation decreases the contribution of the Boltzmann entropy.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We derive the $T\overline{T}$-perturbed version of two-dimensional $q$-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity.	contribution 0.71	0.96	0.13	asserted 1.00
s1	We show that the $T\overline{T}$-deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large $N$ factorization into chiral and anti-chiral sectors.	result 1.00	0.95	0.29	asserted 1.00
s2	For the $U(N)$ gauge theory on the sphere, we show that the large $N$ phase transition persists, and that it is of third order and induced by instantons.	result 1.00	0.96	0.21	asserted 1.00
s3	The effect of the $T\overline{T}$-deformation is to decrease the critical value of the 't Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs.	result 1.00	0.94	0.19	asserted 1.00
s4	The same results are shown to hold for $(q,t)$-deformed Yang-Mills theory.	result 0.89	0.90	0.08	asserted 1.00
s5	We also explicitly evaluate the entanglement entropy in the large $N$ limit of Yang-Mills theory, showing that the $T\overline{T}$-deformation decreases the contribution of the Boltzmann entropy.	result 0.86	0.95	0.11	asserted 1.00

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Original abstract

We derive the $T\overline{T}$-perturbed version of two-dimensional $q$-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the $T\overline{T}$-deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large $N$ factorization into chiral and anti-chiral sectors. For the $U(N)$ gauge theory on the sphere, we show that the large $N$ phase transition persists, and that it is of third order and induced by instantons. The effect of the $T\overline{T}$-deformation is to decrease the critical value of the 't Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for $(q,t)$-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large $N$ limit of Yang-Mills theory, showing that the $T\overline{T}$-deformation decreases the contribution of the Boltzmann entropy.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Metric approach to a $\mathrm{T}\bar{\mathrm{T}}-$like deformation in arbitrary dimensions
hep-th 2022-06 conditional novelty 6.0 of 10

A family of stress-tensor bilinear deformations in d dimensions is shown to be dynamically equivalent to a field-dependent metric flow, with exact metric and vierbein solutions for d=4 abelian gauge theories.
A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
hep-th 2019-04 accept novelty 2.0 of 10

A lecture-note review that derives the deformed Lagrangian, the Burgers-equation spectrum, modular properties of the torus partition function, and the gravity and holographic readings of T-Tbar deformation in two dimensions.

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13 arXiv papers cite this in 19 sentences

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Papers citing it · 11 sentences without a confident label

Compares with it 1 paper

Notice that this is also the expression of the deformed energy density of a Yang-Mills theory in $=2$ [ref] . * it would be interesting to look for a match between the series expansion of the metric proposed here and the perturbative results obtained in [ref] for the Lagrangians associated to abelian gauge theories in $d∈2N$ deformed by the operator $_^[2/d,d]$.[We thank Hossein Babaei-Aghbolagh for suggesting to us the possibility to perform this comparison.]

Metric approach to a $\mathrm{T}\bar{\mathrm{T}}-$like deformation in arbitrary dimensions · Case $r=2/$ · 0.87

Cites it as background 7 papers

In the context of the $TT̅$ deformation, Yang–Mills theory was studied in [ref] and its large-$N$ limit was explored in [ref] .

Exact $T\bar{T}$-deformation of two-dimensional Yang-Mills theory on the sphere · Introduction · 0.84
Other developments in $TT̅$ deformation include but are not limited to [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] .

Comments on large central charge $T\bar{T}$ deformed conformal field theory and cutoff AdS holography · Introduction · 1.00
These deformations also attracts much further attention from both field theory [ref] and holographic perspectives [ref] .

Note on higher-point correlation functions of the $T\bar{T}$ or $J\bar{T}$ deformed CFTs · Introduction · 0.88

What it cites · 137 sentences without a confident label

Builds on 8 papers

A central point of this paper is a generalization of the analysis of [ref] to the large $N$ limit of the $TT$-deformation of $q$-deformed $U(N)$ Yang-Mills theory on the sphere.

Large $N$ phase transition in $T \overline{T}$-deformed $2d$ Yang-Mills theory on the sphere · Introduction · 1.00
The complete analysis for $q$-Yang-Mills theory was carried out in [ref] , and we show how it is adapted to the $T T$-deformed theory in Appendix [ref].

Topological strings and large N phase transitions I: Nonchiral expansion of q-deformed Yang-Mills theory · Instanton analysis · 0.96
The complete analysis for $q$-Yang-Mills theory was carried out in [ref] , and we show how it is adapted to the $T T$-deformed theory in Appendix [ref].

Phase transitions in q-deformed 2d Yang-Mills theory and topological strings · Instanton analysis · 0.96

Uses the method or tool of 7 papers

We solve the saddle point equation [ref] perturbatively, as in [ref] and reviewed in Section [ref] above.

Large $N$ phase transition in $T \overline{T}$-deformed $2d$ Yang-Mills theory on the sphere · Large $N$ limit of $T T$-deformed $q$-Yang-Mills theory · 0.99
Following [ref] , in the case at hand we define [equation] which is the probability of finding a given configuration of weights $h⃗ ∈ℤ^N$, with variables as defined in [ref], where we recall that $Δ(h⃗)$ is the Vandermonde determinant [ref].

Entanglement entropy and the large $N$ expansion of two-dimensional Yang-Mills theory · Entanglement entropy at large $N$ · 0.92
However, it was noted in [ref] that [ref] can be solved perturbatively in $τ$, with the zeroth order being the DK solution [ref] .

Large $N$ Phase Transition in Continuum QCD$_2$ · Strategy · 0.92

Compares with 8 papers

Below we will provide a more extensive comparison between the present analysis and that of [ref] , and this technical aspect will play an important role.

$T\bar{T}$ deformed YM$_{2}$ on general backgrounds from an integral transformation · $T T$-deformation of almost topological gauge theories · 0.91
The crucial difference between the picture of [ref] and its $T T$-deformed version lays in the interpretation of the Casimir in terms of free fermions.

Conformal Field Theory Techniques for Large N Group Theory · Free fermion formulation · 0.88
At this point we notice that, as expected, [ref] is the same equation found in [ref] , except for the renormalization $p ↦p b_q,∞$.

A DK Phase Transition in q-Deformed Yang-Mills on S^2 and Topological Strings · Instanton analysis · 0.97

Cites as background 51 papers

Two-dimensional $U(N)$ Yang-Mills theory on $𝕊^2$ undergoes a third order phase transition [ref] , henceforth called the Douglas-Kazakov (DK) transition, which is induced by instanton instabilities [ref] .

Instanton Induced Large $N$ Phase Transitions in Two and Four Dimensional QCD · Phase transitions in $T T$-deformed $q$-Yang-Mills theory · 0.92
Two-dimensional $U(N)$ Yang-Mills theory on $𝕊^2$ undergoes a third order phase transition [ref] , henceforth called the Douglas-Kazakov (DK) transition, which is induced by instanton instabilities [ref] .

Large $N$ Phase Transition in Continuum QCD$_2$ · Phase transitions in $T T$-deformed $q$-Yang-Mills theory · 0.92
Recent broad interest has been attracted to the solvable irrelevant deformation by the $TT$ operator, which is present in any local relativistic two-dimensional quantum field theory, that was identified by [ref] (see [ref] for a review).

On space of integrable quantum field theories · Introduction · 1.00

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