{"arxiv_id":"2009.00657","incoming":{"papers":13,"sentences":19,"groups":[{"kind":"comparison","label":"Compares with it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2206.03415","title":"Metric approach to a $\\mathrm{T}\\bar{\\mathrm{T}}-$like deformation in arbitrary dimensions","url":"/paper/2206.03415","section":"Case $r=2/$","sentence":"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.]","intent_p":0.87,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":7,"sentences":7,"quotes":[{"arxiv_id":"2207.05095","title":"Exact $T\\bar{T}$-deformation of two-dimensional Yang-Mills theory on the sphere","url":"/paper/2207.05095","section":"Introduction","sentence":"In the context of the $TT̅$ deformation, Yang–Mills theory was studied in [ref] and its large-$N$ limit was explored in [ref] .","intent_p":0.84,"contests_p":null},{"arxiv_id":"2012.14414","title":"Comments on large central charge $T\\bar{T}$ deformed conformal field theory and cutoff AdS holography","url":"/paper/2012.14414","section":"Introduction","sentence":"Other developments in $TT̅$ deformation include but are not limited to [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2012.06202","title":"Note on higher-point correlation functions of the $T\\bar{T}$ or $J\\bar{T}$ deformed CFTs","url":"/paper/2012.06202","section":"Introduction","sentence":"These deformations also attracts much further attention from both field theory [ref] and holographic perspectives [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"2403.03119","title":"Higher form symmetries and orbifolds of two-dimensional Yang-Mills theory","url":"/paper/2403.03119","section":"TT-deformation","sentence":"The irrelevant perturbation of two-dimensional Yang–Mills theory by the operator $T T$ was considered in [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"2203.09683","title":"Exact $T\\overline{T}$ deformation of two-dimensional Maxwell theory","url":"/paper/2203.09683","section":"Introduction","sentence":"The $TT$ deformation of Yang–Mills theory has been already considered in [ref] , mainly in relation to the large-$N$ limit for the sphere topology.","intent_p":0.91,"contests_p":null}]}],"unlabelled_sentences":11},"outgoing":{"papers":87,"sentences":222,"groups":[{"kind":"extends","label":"Builds on","papers":8,"sentences":8,"quotes":[{"arxiv_id":"1810.05404","title":"Large $N$ phase transition in $T \\overline{T}$-deformed $2d$ Yang-Mills theory on the sphere","url":"/paper/1810.05404","section":"Introduction","sentence":"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.","intent_p":1.0,"contests_p":null},{"arxiv_id":"hep-th/0509041","title":"Topological strings and large N phase transitions I: Nonchiral expansion of q-deformed Yang-Mills theory","url":"/paper/hep-th/0509041","section":"Instanton analysis","sentence":"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].","intent_p":0.96,"contests_p":null},{"arxiv_id":"hep-th/0509002","title":"Phase transitions in q-deformed 2d Yang-Mills theory and topological strings","url":"/paper/hep-th/0509002","section":"Instanton analysis","sentence":"The complete analysis for $q$-Yang-Mills theory was carried out in [ref] , and we show how it is adapted to the $T 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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].","intent_p":0.92,"contests_p":null},{"arxiv_id":"hep-th/9305047","title":"Large $N$ Phase Transition in Continuum QCD$_2$","url":"/paper/hep-th/9305047","section":"Strategy","sentence":"However, it was noted in [ref] that [ref] can be solved perturbatively in $τ$, with the zeroth order being the DK solution [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"hep-th/9310144","title":"Lectures on 2d Gauge Theories: Topological Aspects and Path Integral Techniques","url":"/paper/hep-th/9310144","section":"$T T$-deformation of two-dimensional Yang-Mills theory","sentence":"From this point, the derivation of the heat kernel expansion using abelianization of the path integrals goes exactly as in [ref] : one conjugates the scalar field $ϕ$ into a Cartan subalgebra of $$ using gauge invariance and the Weyl integral formula, and then integrates over the root components $A_α$ of the gauge connections with respect to the root space decomposition of the Lie algebra $$.","intent_p":0.86,"contests_p":null},{"arxiv_id":"hep-th/0509002","title":"Phase transitions in q-deformed 2d Yang-Mills theory and topological strings","url":"/paper/hep-th/0509002","section":"Complete instanton partition function","sentence":"However, we stress that, for each instanton sector $ℓ⃗$, every order in the perturbative expansion can in principle be evaluated with the generalization of the strategy of [ref] that we have just sketched.","intent_p":0.81,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":8,"sentences":12,"quotes":[{"arxiv_id":"1912.04686","title":"$T\\bar{T}$ deformed YM$_{2}$ on general backgrounds from an integral transformation","url":"/paper/1912.04686","section":"$T T$-deformation of almost topological gauge theories","sentence":"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.","intent_p":0.91,"contests_p":null},{"arxiv_id":"hep-th/9303159","title":"Conformal Field Theory Techniques for Large N Group Theory","url":"/paper/hep-th/9303159","section":"Free fermion formulation","sentence":"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.","intent_p":0.88,"contests_p":null},{"arxiv_id":"hep-th/0509004","title":"A DK Phase Transition in q-Deformed Yang-Mills on S^2 and Topological Strings","url":"/paper/hep-th/0509004","section":"Instanton analysis","sentence":"At this point we notice that, as expected, [ref] is the same equation found in [ref] , except for the renormalization $p ↦p b_q,∞$.","intent_p":0.97,"contests_p":null},{"arxiv_id":"hep-th/0509002","title":"Phase transitions in q-deformed 2d Yang-Mills theory and topological 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theory","sentence":"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] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"hep-th/9305047","title":"Large $N$ Phase Transition in Continuum QCD$_2$","url":"/paper/hep-th/9305047","section":"Phase transitions in $T T$-deformed $q$-Yang-Mills theory","sentence":"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] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"1608.05499","title":"On space of integrable quantum field theories","url":"/paper/1608.05499","section":"Introduction","sentence":"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).","intent_p":1.0,"contests_p":null},{"arxiv_id":"1904.13376","title":"A pedagogical review on solvable irrelevant deformations of 2d quantum field theory","url":"/paper/1904.13376","section":"Introduction","sentence":"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).","intent_p":1.0,"contests_p":null},{"arxiv_id":"1608.05534","title":"$T \\bar{T}$-deformed 2D Quantum Field Theories","url":"/paper/1608.05534","section":"Introduction","sentence":"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 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