Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2511.13597

$T\bar{T}$ Deformations and Form Factor Program

Olalla A. Castro-Alvaredo, Stefano Negro, Fabio Sailis

Published Nov 17, 2025• 0 citations
arXivHTMLPDF

Abstract

In this proceeding contribution, we review a recently proposed method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by irrelevant fields of the $T\bar{T}$ family. Our construction generalizes standard form factor techniques to deal with the deformed two-body scattering amplitudes, which are typical in this setting. The results are minimal form factors which are the product of the undeformed solution and a new function. This function can be fixed by requiring constant asymptotics for large rapidities, smoothness in the limit when the perturbation parameters go to zero, and agreement with standard MFF formulae for particular choices of the perturbation couplings. We observe that, for a certain range of parameters, the new MFF develops a pole at $θ=0$. By considering several UV-complete theories, we argue that such poles can emerge naturally from the MFF integral representation and suggest how they may be eliminated.

DOI
10.48550/arxiv.2511.13597

Related papers

T ${\bar {\rm T}}$ T ¯ Deformations and Form Factor Program

Olalla A. Castro-Alvaredo, Stefano Negro, Fabio Sailis

Abstract In this proceeding contribution, we review a recently proposed method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by irrelevant fields of the T ${\bar {\rm T}}$ T ¯ family. Our construction generalizes standard form factor techniques to deal with the deformed two-body scattering amplitudes, which are typical in this setting. The results are minimal form factors which are the product of the undeformed solution and a new function. This function can be fixed by requiring constant asymptotics for large rapidities, smoothness in the limit when the perturbation parameters go to zero, and agreement with standard MFF formulae for particular choices of the perturbation couplings. We observe that, for a certain range of parameters, the new MFF develops a pole at θ = 0. By considering several UV-complete theories, we argue that such poles can emerge naturally from the MFF integral representation and suggest how they may be eliminated.

Journal of Physics Conference Series•Dec 1, 2025•0 citations

TT¯ Deformations and Form Factor Program

Olalla A. Castro-Alvaredo, Stefano Negro, Fabio Sailis

In this proceeding contribution, we review a recently proposed method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by irrelevant fields of the TT¯ family. Our construction generalizes standard form factor techniques to deal with the deformed two-body scattering amplitudes, which are typical in this setting. The results are minimal form factors which are the product of the undeformed solution and a new function. This function can be fixed by requiring constant asymptotics for large rapidities, smoothness in the limit when the perturbation parameters go to zero, and agreement with standard MFF formulae for particular choices of the perturbation couplings. We observe that, for a certain range of parameters, the new MFF develops a pole at θ = 0. By considering several UV-complete theories, we argue that such poles can emerge naturally from the MFF integral representation and suggest how they may be eliminated.

•Dec 5, 2025•0 citations

Complete minimal form factors for irrelevant deformations of integrable quantum field theory

Castro-Alvaredo, Olalla A., Sailis, Fabio, Stefano Negro

In this paper, we present a method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by generalized TTbar perturbations. Building on existing results by the same authors, these MFFs are constructed in such a way as not to allow for any free parameters, an issue that plagued previous solutions. The MFFs are derived from a generalization of the standard integral representation which has been used for UV-complete theories since the birth of the form factor bootstrap program. By UV-complete we mean theories whose short-distance/high-energy limit is a local conformal field theory. Their asymptotics is characterized by exponential decay at large rapidities. By computing higher particle form factors, we find that any natural higher-particle solutions involve the cancellation of parts of the newly found MFF. We conclude that the assumption that the form factor equations, particularly the kinematic residue equation, remain unchanged in the presence of TTbar perturbations, is too strong. There is a trade-off between having MFFs satisfying desirable analyticity and asymptotic properties and finding analytic solutions to the form factor equations, which is likely solved by nontrivial changes to the form factor equations, especially those where locality or semilocality of fields are essential assumptions.

•Oct 2, 2025•0 citations

Complete minimal form factors for irrelevant deformations of integrable quantum field theory

Fabio Sailis, Olalla A. Castro-Alvaredo, Stefano Negro

In this paper, we present a method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by generalized T T ¯ perturbations. Building on existing results by the same authors, these MFFs are constructed in such a way as not to allow for any free parameters, an issue that plagued previous solutions. The MFFs are derived from a generalization of the standard integral representation which has been used for UV-complete theories since the birth of the form factor bootstrap program. By UV-complete we mean theories whose short-distance/high-energy limit is a local conformal field theory. Their asymptotics is characterized by exponential decay at large rapidities. By computing higher particle form factors, we find that any natural higher-particle solutions involve the cancellation of parts of the newly found MFF. We conclude that the assumption that the form factor equations, particularly the kinematic residue equation, remain unchanged in the presence of T T ¯ perturbations, is too strong. There is a trade-off between having MFFs satisfying desirable analyticity and asymptotic properties and finding analytic solutions to the form factor equations, which is likely solved by nontrivial changes to the form factor equations, especially those where locality or semilocality of fields are essential assumptions.

arXiv:2506.20517•Nuclear Physics B•Sep 22, 2025•0 citations

Completing the Bootstrap Program for $\mathrm{T}\bar{\mathrm{T}}$-Deformed Massive Integrable Quantum Field Theories

Olalla A. Castro-Alvaredo, Stefano Negro, Fabio Sailis

In recent years a considerable amount of attention has been devoted to the investigation of 2D quantum field theories perturbed by certain types of irrelevant operators. These are the composite field $\mathrm{T}\bar{\mathrm{T}}$ - constructed out of the components of the stress-energy tensor - and its generalisations - built from higher-spin conserved currents. The effect of such perturbations on the infrared and ultraviolet properties of the theory has been extensively investigated. In the context of integrable quantum field theories, a fruitful perspective is that of factorised scattering theory. In fact, the above perturbations were shown to preserve integrability. The resulting deformed scattering matrices - extensively analysed with the thermodynamic Bethe ansatz - provide the first step in the development of a complete bootstrap program. In this letter we present a systematic approach to computing matrix elements of operators in generalised $\mathrm{T}\bar{\mathrm{T}}$-perturbed models, based on employing the standard form factor program. Our approach is very general and can be applied to all theories with diagonal scattering. We show that the deformed form factors, just as happens for the $S$-matrix, factorise into the product of the undeformed ones and of a perturbation- and theory-dependent term. From these solutions, correlation functions can be obtained and their asymptotic properties studied. Our results set the foundations of a new research program for massive integrable quantum field theory perturbed by irrelevant operators.

arXiv:2305.17068•May 26, 2023•1 citation

Completing the bootstrap program for T T ― -deformed massive integrable quantum field theories

Olalla A. Castro-Alvaredo, Stefano Negro, Fabio Sailis

Abstract In recent years a considerable amount of attention has been devoted to the investigation of 2D quantum field theories perturbed by certain types of irrelevant operators. These are the composite field T T ― —constructed out of the components of the stress-energy tensor—and its generalisations—built from higher-spin conserved currents. The effect of such perturbations on the infrared and ultraviolet properties of the theory has been extensively investigated. In the context of integrable quantum field theories, a fruitful perspective is that of factorised scattering theory. In fact, the above perturbations were shown to preserve integrability. The resulting deformed scattering matrices—extensively analysed with the thermodynamic Bethe ansatz—provide the first step in the development of a bootstrap program. In this paper we present a systematic approach to computing matrix elements of operators in generalised T T ― -perturbed models, based on employing the standard form factor program. We show that for theories with diagonal scattering and certain types of fields the deformed form factors, factorise into the product of the undeformed ones and of a perturbation- and theory-dependent term. From these solutions, correlation functions can be obtained and their asymptotic properties studied.

Journal of Physics A Mathematical and Theoretical•Jun 3, 2024•6 citations
TTˉT\bar{T}TTˉ Deformations and Form Factor Program
In this proceeding contribution, we review a recently proposed method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by irrelevant fields of the TTˉT\bar{T}TTˉ family. Our construction generalizes standard form factor techniques to deal with the deformed two-body scattering amplitudes, which are typical in this setting. The results are minimal form factors which are the product of the undeformed solution and a new function. This function can be fixed by requiring constant asymptotics for large rapidities, smoothness in the limit when the perturbation parameters go to zero, and agreement with standard MFF formulae for particular choices of the perturbation couplings. We observe that, for a certain range of parameters, the new MFF develops a pole at θ=0θ=0θ=0. By considering several UV-complete theories, we argue that such poles can emerge naturally from the MFF integral representation and suggest how they may be eliminated.
T Tˉ{\bar {\rm T}}Tˉ T ¯ Deformations and Form Factor Program
Abstract In this proceeding contribution, we review a recently proposed method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by irrelevant fields of the T Tˉ{\bar {\rm T}}Tˉ T ¯ family. Our construction generalizes standard form factor techniques to deal with the deformed two-body scattering amplitudes, which are typical in this setting. The results are minimal form factors which are the product of the undeformed solution and a new function. This function can be fixed by requiring constant asymptotics for large rapidities, smoothness in the limit when the perturbation parameters go to zero, and agreement with standard MFF formulae for particular choices of the perturbation couplings. We observe that, for a certain range of parameters, the new MFF develops a pole at θ = 0. By considering several UV-complete theories, we argue that such poles can emerge naturally from the MFF integral representation and suggest how they may be eliminated.
In this proceeding contribution, we review a recently proposed method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by irrelevant fields of the TT¯ family. Our construction generalizes standard form factor techniques to deal with the deformed two-body scattering amplitudes, which are typical in this setting. The results are minimal form factors which are the product of the undeformed solution and a new function. This function can be fixed by requiring constant asymptotics for large rapidities, smoothness in the limit when the perturbation parameters go to zero, and agreement with standard MFF formulae for particular choices of the perturbation couplings. We observe that, for a certain range of parameters, the new MFF develops a pole at θ = 0. By considering several UV-complete theories, we argue that such poles can emerge naturally from the MFF integral representation and suggest how they may be eliminated.
In this paper, we present a method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by generalized TTbar perturbations. Building on existing results by the same authors, these MFFs are constructed in such a way as not to allow for any free parameters, an issue that plagued previous solutions. The MFFs are derived from a generalization of the standard integral representation which has been used for UV-complete theories since the birth of the form factor bootstrap program. By UV-complete we mean theories whose short-distance/high-energy limit is a local conformal field theory. Their asymptotics is characterized by exponential decay at large rapidities. By computing higher particle form factors, we find that any natural higher-particle solutions involve the cancellation of parts of the newly found MFF. We conclude that the assumption that the form factor equations, particularly the kinematic residue equation, remain unchanged in the presence of TTbar perturbations, is too strong. There is a trade-off between having MFFs satisfying desirable analyticity and asymptotic properties and finding analytic solutions to the form factor equations, which is likely solved by nontrivial changes to the form factor equations, especially those where locality or semilocality of fields are essential assumptions.
In this paper, we present a method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by generalized T T ¯ perturbations. Building on existing results by the same authors, these MFFs are constructed in such a way as not to allow for any free parameters, an issue that plagued previous solutions. The MFFs are derived from a generalization of the standard integral representation which has been used for UV-complete theories since the birth of the form factor bootstrap program. By UV-complete we mean theories whose short-distance/high-energy limit is a local conformal field theory. Their asymptotics is characterized by exponential decay at large rapidities. By computing higher particle form factors, we find that any natural higher-particle solutions involve the cancellation of parts of the newly found MFF. We conclude that the assumption that the form factor equations, particularly the kinematic residue equation, remain unchanged in the presence of T T ¯ perturbations, is too strong. There is a trade-off between having MFFs satisfying desirable analyticity and asymptotic properties and finding analytic solutions to the form factor equations, which is likely solved by nontrivial changes to the form factor equations, especially those where locality or semilocality of fields are essential assumptions.
Completing the Bootstrap Program for TTˉ\mathrm{T}\bar{\mathrm{T}}TTˉ-Deformed Massive Integrable Quantum Field Theories
In recent years a considerable amount of attention has been devoted to the investigation of 2D quantum field theories perturbed by certain types of irrelevant operators. These are the composite field TTˉ\mathrm{T}\bar{\mathrm{T}}TTˉ - constructed out of the components of the stress-energy tensor - and its generalisations - built from higher-spin conserved currents. The effect of such perturbations on the infrared and ultraviolet properties of the theory has been extensively investigated. In the context of integrable quantum field theories, a fruitful perspective is that of factorised scattering theory. In fact, the above perturbations were shown to preserve integrability. The resulting deformed scattering matrices - extensively analysed with the thermodynamic Bethe ansatz - provide the first step in the development of a complete bootstrap program. In this letter we present a systematic approach to computing matrix elements of operators in generalised TTˉ\mathrm{T}\bar{\mathrm{T}}TTˉ-perturbed models, based on employing the standard form factor program. Our approach is very general and can be applied to all theories with diagonal scattering. We show that the deformed form factors, just as happens for the SSS-matrix, factorise into the product of the undeformed ones and of a perturbation- and theory-dependent term. From these solutions, correlation functions can be obtained and their asymptotic properties studied. Our results set the foundations of a new research program for massive integrable quantum field theory perturbed by irrelevant operators.
Abstract In recent years a considerable amount of attention has been devoted to the investigation of 2D quantum field theories perturbed by certain types of irrelevant operators. These are the composite field T T ― —constructed out of the components of the stress-energy tensor—and its generalisations—built from higher-spin conserved currents. The effect of such perturbations on the infrared and ultraviolet properties of the theory has been extensively investigated. In the context of integrable quantum field theories, a fruitful perspective is that of factorised scattering theory. In fact, the above perturbations were shown to preserve integrability. The resulting deformed scattering matrices—extensively analysed with the thermodynamic Bethe ansatz—provide the first step in the development of a bootstrap program. In this paper we present a systematic approach to computing matrix elements of operators in generalised T T ― -perturbed models, based on employing the standard form factor program. We show that for theories with diagonal scattering and certain types of fields the deformed form factors, factorise into the product of the undeformed ones and of a perturbation- and theory-dependent term. From these solutions, correlation functions can be obtained and their asymptotic properties studied.