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:2608.09776

Schwinger-Keldysh effective field theory of type-B Goldstone: near-diagonal geometry and Berry term

Pei Zheng, Mei Huang

Published Aug 10, 2026• 0 citations
arXivHTMLPDF

Abstract

In this work, we formulate a finite temperature Schwinger-Keldysh effective field theory for type-B Goldstone modes based on geometric objects globally defined on the coset manifold. In particular, after taking the classical limit, we organize the required two time contour structure by a near-diagonal geometry in which the $r$-type field is interpreted as the physical Goldstone configuration and the $a$-type field is identified as corresponding tangent displacement. Within this geometric viewpoint, the Berry term essential for type-B Goldstones is obtained directly through the transgression of the Berry curvature. Moreover, we show that this exact Berry transgression is compatible with dynamical KMS condition. In order to construct the conservative, dissipative and noise sectors, we classify possible tensors globally defined on the coset manifold. Based on this framework, we discuss in detail two concrete model examples. The dispersion relations of the Goldstone modes and the associated two-point correlation functions are calculated in the presence of dissipation.

DOI
10.48550/arxiv.2608.09776

Related papers

The Schwinger-Keldysh coset construction

Can Onur Akyuz, Garrett L. Goon, Riccardo Penco

A bstract The coset construction is a tool for systematically building low energy effective actions for Nambu-Goldstone modes. This technique is typically used to compute time-ordered correlators appropriate for S -matrix computations for systems in their ground state. In this paper, we extend this technique to the Schwinger-Keldysh formalism, which enables one to calculate a wider variety of correlators and applies also to systems in a mixed state. We focus our attention on internal symmetries and demonstrate that, after identifying the appropriate symmetry breaking pattern, Schwinger-Keldysh effective actions for Nambu-Goldstone modes can be constructed using the standard rules of the coset construction. Particular emphasis is placed on the thermal state and ensuring that correlators satisfy the KMS relation. We also discuss explicitly the power counting scheme underlying our effective actions. We comment on the similarities and differences between our approach and others that have previously appeared in the literature. In particular, our prescription does not require the introduction of additional “diffusive” symmetries and retains the full non-linear structure generated by the coset construction. We conclude with a series of explicit examples, including a computation of the finite-temperature two-point functions of conserved spin currents in non-relativistic paramagnets, antiferromagnets, and ferromagnets. Along the way, we also clarify the discrete symmetries that set antiferromagnets apart from ferromagnets, and point out that the dynamical KMS symmetry must be implemented in different ways in these two systems.

arXiv:2306.17232•Journal of High Energy Physics•Jun 4, 2024•22 citations

Three-point functions from a Schwinger-Keldysh effective action, resummed in derivatives

Navid Abbasi, Dirk H. Rischke

The search for the conjectured QCD critical point in heavy-ion collisions requires to account for far-from equilibrium effects as well as fluctuations, and in particular non-Gaussian fluctuations, in the modeling of the dynamics of the hot and dense matter created in such collisions. In order to study far-from equilibrium effects as well as fluctuations, in this work we construct a Schwinger-Keldysh effective field theory (EFT) for the diffusion of the density to all orders in derivatives. The dissipation in the free part of our EFT follows the Boltzmann equation in the relaxation-time approximation (RTA). The interaction part of the EFT is constructed based on the self-interaction of the density field. We analytically find the quadratic and cubic parts of the KMS-invariant EFT in closed form, resummed in derivatives. We then explicitly compute the symmetrized three-point function at tree level, and investigate its analytical structure in detail. We also analytically calculate the branch-point singularity that appears in the structure of the two-point response function due to loop effects. Our results are important for future studies of the real-time dynamics of the correlation functions and the possible relation to thermalization when the system is far from equilibrium.

Journal of High Energy Physics•Jan 1, 2025•0 citations

Three-point functions from a Schwinger-Keldysh effective action, resummed in derivatives

Navid Abbasi, Dirk H. Rischke

The search for the conjectured QCD critical point in heavy-ion collisions requires to account for far-from equilibrium effects as well as fluctuations, and in particular non-Gaussian fluctuations, in the modeling of the dynamics of the hot and dense matter created in such collisions. In order to study far-from equilibrium effects as well as fluctuations, in this work we construct a Schwinger-Keldysh effective field theory (EFT) for the diffusion of the density to all orders in derivatives. The dissipation in the free part of our EFT follows the Boltzmann equation in the relaxation-time approximation (RTA). The interaction part of the EFT is constructed based on the self-interaction of the density field. We analytically find the quadratic and cubic parts of the KMS-invariant EFT in closed form, resummed in derivatives. We then explicitly compute the symmetrized three-point function at tree level, and investigate its analytical structure in detail. We also analytically calculate the branch-point singularity that appears in the structure of the two-point response function due to loop effects. Our results are important for future studies of the real-time dynamics of the correlation functions and the possible relation to thermalization when the system is far from equilibrium.

arXiv:2410.07929•Oct 10, 2024•1 citation

Three-point functions from a Schwinger-Keldysh effective action, resummed in derivatives

Navid Abbasi, Dirk H. Rischke

A bstract The search for the conjectured QCD critical point in heavy-ion collisions requires to account for far-from equilibrium effects as well as fluctuations, and in particular non-Gaussian fluctuations, in the modeling of the dynamics of the hot and dense matter created in such collisions. In order to study far-from equilibrium effects as well as fluctuations, in this work we construct a Schwinger-Keldysh effective field theory (EFT) for the diffusion of the density to all orders in derivatives. The dissipation in the free part of our EFT follows the Boltzmann equation in the relaxation-time approximation (RTA). The interaction part of the EFT is constructed based on the self-interaction of the density field. We analytically find the quadratic and cubic parts of the KMS-invariant EFT in closed form, resummed in derivatives. We then explicitly compute the symmetrized three-point function at tree level, and investigate its analytical structure in detail. We also analytically calculate the branch-point singularity that appears in the structure of the two-point response function due to loop effects. Our results are important for future studies of the real-time dynamics of the correlation functions and the possible relation to thermalization when the system is far from equilibrium.

Journal of High Energy Physics•May 28, 2025•3 citations

Quantum fluctuations in hydrodynamics and quantum long-time tails

Akash Jain

We construct a quantum Schwinger-Keldysh (SK) effective field theory for the diffusive hydrodynamics of a conserved scalar field. Quantum corrections within the SK framework are guided by fluctuation-dissipation relations, enforced via a dynamical Kubo-Martin-Schwinger (KMS) symmetry. We find that the KMS symmetry necessarily generates fluctuation contributions in the SK effective action at all orders in the noise field, thereby giving rise to intrinsically non-Gaussian noise. We use our results to compute one-loop quantum corrections to the two-point density-density retarded correlation function, leading to a quantum generalization of hydrodynamic long-time tails. Our results apply at arbitrarily high orders in $\hbar$. The one-loop results for retarded correlation functions have been expressed in terms of a family of polynomials. We also provide a closed-form expression for the one-loop results at leading order in the wavevector expansion.

hep-thCross-listedarXiv:2601.22140•SciPost Physics•Jan 30, 2026•0 citations

Universality of pseudo-Goldstone damping near critical points

Yang-yang Tan, Yongrui Chen, Wei‐jie Fu +1 more

Real-time dynamics of strongly correlated systems, in particular its critical dynamics near phase transitions, have been always on the cutting edge of studies in diverse fields of physics, e.g., high energy physics, condensed matter, holography, etc. In this work, we investigate the critical damping of collective modes associated with spontaneous breaking of approximate symmetries, which are called pseudo-Goldstone modes, in strongly correlated systems. Using the Schwinger-Keldysh field theory, we find a universal pseudo-Goldstone damping via the critical O(N) model that has never been found before by other approaches. Different from the conventional damping found in holography and hydrodynamics, the new one is controlled by critical fluctuations, hence is invisible in mean-field systems or strongly correlated systems with classical gravity duals. Since the critical damping depends solely on the universalities of the critical point, irrespective of the microscopic details, our conclusion should be applicable to a wide class of interacting systems. Strongly correlated systems exhibit universal dynamics near phase transitions, from particle to condensed matter physics. However, despite the successes of various theoretical approaches, systematic treatments of fluctuations are scarce. Here the authors unveil a universal damping of pseudo-Goldstone modes in systems with approximate symmetries, advancing our understanding of near-critical dynamics in several contexts.

arXiv:2403.03503•Nature Communications•Mar 25, 2025•6 citations
In this work, we formulate a finite temperature Schwinger-Keldysh effective field theory for type-B Goldstone modes based on geometric objects globally defined on the coset manifold. In particular, after taking the classical limit, we organize the required two time contour structure by a near-diagonal geometry in which the rrr-type field is interpreted as the physical Goldstone configuration and the aaa-type field is identified as corresponding tangent displacement. Within this geometric viewpoint, the Berry term essential for type-B Goldstones is obtained directly through the transgression of the Berry curvature. Moreover, we show that this exact Berry transgression is compatible with dynamical KMS condition. In order to construct the conservative, dissipative and noise sectors, we classify possible tensors globally defined on the coset manifold. Based on this framework, we discuss in detail two concrete model examples. The dispersion relations of the Goldstone modes and the associated two-point correlation functions are calculated in the presence of dissipation.
A bstract The coset construction is a tool for systematically building low energy effective actions for Nambu-Goldstone modes. This technique is typically used to compute time-ordered correlators appropriate for S -matrix computations for systems in their ground state. In this paper, we extend this technique to the Schwinger-Keldysh formalism, which enables one to calculate a wider variety of correlators and applies also to systems in a mixed state. We focus our attention on internal symmetries and demonstrate that, after identifying the appropriate symmetry breaking pattern, Schwinger-Keldysh effective actions for Nambu-Goldstone modes can be constructed using the standard rules of the coset construction. Particular emphasis is placed on the thermal state and ensuring that correlators satisfy the KMS relation. We also discuss explicitly the power counting scheme underlying our effective actions. We comment on the similarities and differences between our approach and others that have previously appeared in the literature. In particular, our prescription does not require the introduction of additional “diffusive” symmetries and retains the full non-linear structure generated by the coset construction. We conclude with a series of explicit examples, including a computation of the finite-temperature two-point functions of conserved spin currents in non-relativistic paramagnets, antiferromagnets, and ferromagnets. Along the way, we also clarify the discrete symmetries that set antiferromagnets apart from ferromagnets, and point out that the dynamical KMS symmetry must be implemented in different ways in these two systems.
The search for the conjectured QCD critical point in heavy-ion collisions requires to account for far-from equilibrium effects as well as fluctuations, and in particular non-Gaussian fluctuations, in the modeling of the dynamics of the hot and dense matter created in such collisions. In order to study far-from equilibrium effects as well as fluctuations, in this work we construct a Schwinger-Keldysh effective field theory (EFT) for the diffusion of the density to all orders in derivatives. The dissipation in the free part of our EFT follows the Boltzmann equation in the relaxation-time approximation (RTA). The interaction part of the EFT is constructed based on the self-interaction of the density field. We analytically find the quadratic and cubic parts of the KMS-invariant EFT in closed form, resummed in derivatives. We then explicitly compute the symmetrized three-point function at tree level, and investigate its analytical structure in detail. We also analytically calculate the branch-point singularity that appears in the structure of the two-point response function due to loop effects. Our results are important for future studies of the real-time dynamics of the correlation functions and the possible relation to thermalization when the system is far from equilibrium.
The search for the conjectured QCD critical point in heavy-ion collisions requires to account for far-from equilibrium effects as well as fluctuations, and in particular non-Gaussian fluctuations, in the modeling of the dynamics of the hot and dense matter created in such collisions. In order to study far-from equilibrium effects as well as fluctuations, in this work we construct a Schwinger-Keldysh effective field theory (EFT) for the diffusion of the density to all orders in derivatives. The dissipation in the free part of our EFT follows the Boltzmann equation in the relaxation-time approximation (RTA). The interaction part of the EFT is constructed based on the self-interaction of the density field. We analytically find the quadratic and cubic parts of the KMS-invariant EFT in closed form, resummed in derivatives. We then explicitly compute the symmetrized three-point function at tree level, and investigate its analytical structure in detail. We also analytically calculate the branch-point singularity that appears in the structure of the two-point response function due to loop effects. Our results are important for future studies of the real-time dynamics of the correlation functions and the possible relation to thermalization when the system is far from equilibrium.
A bstract The search for the conjectured QCD critical point in heavy-ion collisions requires to account for far-from equilibrium effects as well as fluctuations, and in particular non-Gaussian fluctuations, in the modeling of the dynamics of the hot and dense matter created in such collisions. In order to study far-from equilibrium effects as well as fluctuations, in this work we construct a Schwinger-Keldysh effective field theory (EFT) for the diffusion of the density to all orders in derivatives. The dissipation in the free part of our EFT follows the Boltzmann equation in the relaxation-time approximation (RTA). The interaction part of the EFT is constructed based on the self-interaction of the density field. We analytically find the quadratic and cubic parts of the KMS-invariant EFT in closed form, resummed in derivatives. We then explicitly compute the symmetrized three-point function at tree level, and investigate its analytical structure in detail. We also analytically calculate the branch-point singularity that appears in the structure of the two-point response function due to loop effects. Our results are important for future studies of the real-time dynamics of the correlation functions and the possible relation to thermalization when the system is far from equilibrium.
We construct a quantum Schwinger-Keldysh (SK) effective field theory for the diffusive hydrodynamics of a conserved scalar field. Quantum corrections within the SK framework are guided by fluctuation-dissipation relations, enforced via a dynamical Kubo-Martin-Schwinger (KMS) symmetry. We find that the KMS symmetry necessarily generates fluctuation contributions in the SK effective action at all orders in the noise field, thereby giving rise to intrinsically non-Gaussian noise. We use our results to compute one-loop quantum corrections to the two-point density-density retarded correlation function, leading to a quantum generalization of hydrodynamic long-time tails. Our results apply at arbitrarily high orders in ℏ\hbarℏ. The one-loop results for retarded correlation functions have been expressed in terms of a family of polynomials. We also provide a closed-form expression for the one-loop results at leading order in the wavevector expansion.
Real-time dynamics of strongly correlated systems, in particular its critical dynamics near phase transitions, have been always on the cutting edge of studies in diverse fields of physics, e.g., high energy physics, condensed matter, holography, etc. In this work, we investigate the critical damping of collective modes associated with spontaneous breaking of approximate symmetries, which are called pseudo-Goldstone modes, in strongly correlated systems. Using the Schwinger-Keldysh field theory, we find a universal pseudo-Goldstone damping via the critical O(N) model that has never been found before by other approaches. Different from the conventional damping found in holography and hydrodynamics, the new one is controlled by critical fluctuations, hence is invisible in mean-field systems or strongly correlated systems with classical gravity duals. Since the critical damping depends solely on the universalities of the critical point, irrespective of the microscopic details, our conclusion should be applicable to a wide class of interacting systems. Strongly correlated systems exhibit universal dynamics near phase transitions, from particle to condensed matter physics. However, despite the successes of various theoretical approaches, systematic treatments of fluctuations are scarce. Here the authors unveil a universal damping of pseudo-Goldstone modes in systems with approximate symmetries, advancing our understanding of near-critical dynamics in several contexts.