The correlation function of (1, 1) and (2, 2) supersymmetric theories with $$ T\overline{T} $$ deformation

He, Song; Sun, Jwo‐Shiun; Sun, Yuan

doi:10.1007/jhep04(2020)100

Cited by 44 publications

(37 citation statements)

References 82 publications

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“…In this work, to construct the correlation functions of the CFTs on a torus with a TT deformation, we apply the Ward identity on a torus and do a proper regularization procedure to figure out the correlation functions with TT deformation in terms of the perturbative field theory approach. It can be regarded as a direct generalization of previous studies [58,71] on correlation functions in the TT deformed bosonic and 13 In this section, in order to compare our results to that of [77], we follow the convention in that paper, where the stress tensor on a torus is related to the previous section up to a factor 2π, and the stress tensor on plane T pl is the same as the previous definition; thus, Eq. (16) becomes…”

Section: Conclusion and Discussionmentioning

confidence: 96%

“…Also, it is interesting to investigate the correlation functions of the supersymmetric theories on the torus, as we did in Ref. [71].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Subsequently, the present authors have considered the four-point functions [58]. Also, we generalized this study to the case with a supersymmetric extension [71]. Note that, in the previous studies, these theories were defined on a plane.…”

Section: Introductionmentioning

confidence: 95%

“…(3) by the Ward identity and do the integral over the torus T 2 with the help of a proper regularization scheme. The Ward identity on a torus associated with the energy-momentum tensor, e.g., T orT, has a different structure compared with that on the plane [58,71]. In terms of the perturbative approach, we obtain the correlation functions with TT deformation systematically by using both operator formalism and path integral language following the analysis in Refs.…”

Section: Introductionmentioning

confidence: 99%

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Correlation functions of CFTs on a torus with a TT¯ deformation

Sun

2020

Phys. Rev. D

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In this paper, we investigate the correlation functions of the conformal field theory (CFT) with the TT deformation on a torus in terms of the perturbative CFT approach, which is the extension of the previous investigations on correlation functions defined on a plane. We systematically obtain the first-order correction to the correlation functions of the CFTs with a TT deformation in both operator formalism and path integral language. As a consistency check, we compute the deformed partition function, namely, the zero-point correlation function, up to the first order, which is consistent with results in the literature. Moreover, we obtain a new recursion relation for correlation functions with multiple T's andT's inserted in generic CFTs on a torus. Based on the recursion relations, we study some correlation functions of stress tensors up to the first order under TT deformation.

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Section: Conclusion and Discussionmentioning

confidence: 96%

“…Also, it is interesting to investigate the correlation functions of the supersymmetric theories on the torus, as we did in Ref. [71].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

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Correlation functions of CFTs on a torus with a TT¯ deformation

Sun

2020

Phys. Rev. D

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“…The T T -deformation of Wess-Zumino-Witten (WZW) models was studied from the string theory perspective in the target space theory [18] and also in the gauged worldsheet sigma-model [19]. Supersymmetric extensions were considered by [20][21][22][23][24][25]. Generalized T T -deformations were discussed in [26][27][28], while the extensions to higher-dimensional field theories is considered by [29] using holography, and more recently in [30] from direct analysis of the renormalization group flow equation.…”

Section: Jhep11(2020)086mentioning

confidence: 99%

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

Santilli

Szabo

Tierz

2020

J. High Energ. Phys.

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We derive the $$ T\overline{T} $$ T 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 $$ T\overline{T} $$ T 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 $$ T\overline{T} $$ T 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 $$ T\overline{T} $$ T T ¯ -deformation decreases the contribution of the Boltzmann entropy.

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Non-linear supersymmetry and $$ T\overline{T} $$-like flows

Ferko

Jiang

Sethi

et al. 2020

J. High Energ. Phys.

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The TT deformation of a supersymmetric two-dimensional theory preserves the original supersymmetry. Moreover, in several interesting cases the deformed theory possesses additional non-linearly realized supersymmetries. We show this for certain N = (2, 2) models in two dimensions, where we observe an intriguing similarity with known N = 1 models in four dimensions. This suggests that higher-dimensional models with non-linearly realized supersymmetries might also be obtained from TT -like flow equations.We show that in four dimensions this is indeed the case for N = 1 Born-Infeld theory, as well as for the Goldstino action for spontaneously broken N = 1 supersymmetry. arXiv:1910.01599v1 [hep-th] 3 Oct 2019Contents 1 Introduction 1 2 D = 2 N = (2, 2) Flows and Non-Linear N = (2, 2) Supersymmetry 4 2.1 TT deformations with N = (2, 2) supersymmetry 4 2.2 The TT -deformed twisted-chiral model and partial-breaking 7 2.3 The TT -deformed chiral model and partial-breaking 13 3 D = 4 T 2 Deformations and Their Supersymmetric Extensions 16 3.1 Comments on the T 2 operator in D = 4 16 3.2 D = 4 N = 1 supercurrent-squared operator 18 4 Bosonic Born-Infeld As a T 2 Flow 20 5 Supersymmetric Born-Infeld From Supercurrent-Squared Deformation 22 7 Conclusions and Outlook 33 A Deriving a Useful On-shell Identity 36 construct two models describing the partial supersymmetry breaking pattern N = (4, 4) → N = (2, 2) in D = 2. These models have manifest N = (2, 2) supersymmetry from the superspace structure used in their construction, but they also admit another hidden nonlinear N = (2, 2) supersymmetry. It turns out the resulting actions are exactly the same as the N = (2, 2) chiral and twisted chiral TT -deformed actions of [18]. The intriguing relation between non-linear supersymmetry and TT therefore persists for models with manifest N = (2, 2) supersymmetry. Interestingly, even the D = 2 Volkov-Akulov action, describing the dynamics of the Goldstinos which arise from the spontaneous breaking of N = (2, 2) supersymmetry, satisfies a TT flow equation [21]. This collection of examples motivates us to see whether any higher-dimensional theories with non-linear supersymmetries might also satisfy TT -like flow equations. It has been known for more than two decades that the Bagger-Galperin action for the D = 4 N = 1 Born-Infeld theory describes N = 2 → N = 1 partial supersymmetry breaking [22]. Does the Bagger-Galperin action arise from a TT -like deformation of N = 1 Maxwell theory? That the linear order deformation is given by a supercurrent-squared operator was noted long ago in [23]. Much more recently, bosonic Born-Infeld theory was shown to satisfy a T 2 flow equation, where T 2 is an operator quadratic in the stress-energy tensor [24]. In this work, we explicitly show that the Bagger-Galperin action indeed satisfies a supercurrentsquared flow equation, generalizing the observation of [23] to all orders in the deformation parameter. The supercurrent-squared deformation operator is constructed from supercurrent multiplets, but its to...

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The correlation function of (1, 1) and (2, 2) supersymmetric theories with $$ T\overline{T} $$ deformation

Cited by 44 publications

References 82 publications

Correlation functions of CFTs on a torus with a TT¯ deformation

Correlation functions of CFTs on a torus with a TT¯ deformation

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

Non-linear supersymmetry and $$ T\overline{T} $$-like flows

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