Low-energy Effective Action Research Articles

Derivative four-fermion model, effective action and bumblebee generation

In this paper, we study the one-loop effective potential of a derivative four-fermion model. As a result, an exact bumblebee-like potential is radiatively generated. Afterwards, we generalize our study for a finite temperature case and explicitly demonstrate the possibility of phase transitions allowing for the restoration of the Lorentz symmetry. We also investigate the low-energy effective action, from which we obtain the usual kinetic term and the corresponding bumblebee potential.

What if string theory has a de Sitter excited state?

We propose precise effective field theory criteria to obtain a four-dimensional de Sitter space within M-theory. To this effect, starting with the state space described by the action of metric perturbations, fluxes etc over the supersymmetric Minkowski vacuum in eleven-dimensions, we discuss the most general low energy effective action in terms of the eleven-dimensional fields including non-perturbative and non-local terms. Given this, our criteria to obtain a valid four-dimensional de Sitter solution at far IR involve satisfying the Schwinger-Dyson equations of the associated path integral, as well as obeying positivity constraints on the dual IIA string coupling and its time derivative. For excited states, the Schwinger-Dyson equations imply an effective emergent potential different from the original potential. We show that while vacuum solutions and arbitrary coherent states fail to satisfy these criteria, a specific class of excited states called the Glauber-Sudarshan states obey them. Using the resurgent structure of observables computed using the path integral over the Glauber-Sudarshan states, four-dimensional de Sitter in the flat slicing can be constructed using a Glauber-Sudarshan state in M-theory.Among other novel results, we discuss the smallness of the positive cosmological constant, including the curious case where the cosmological constant is very slowly varying with time. We also discuss the resolution of identity with the Glauber-Sudarshan states, generation and the convergence properties of the non-perturbative and the non-local effects, the problems with the static patch and other related topics. We analyze briefly the issues related to the compatibility of the Wilsonian effective action with Borel resummations and discuss how they influence the effective field theory description in a four-dimensional de Sitter space.

Large D gravity and low D string via α′ corrections

In this paper, we generalize the correspondence between large D gravity and low D string theory to the most general case, including its T-dual solutions. It is well-known that the large D limit of the Schwarzschild-Tangherlini black hole in gravity becomes a two-dimensional near-horizon geometry. Similarly, the large D limit of its T-dual solution, obtained by the Buscher rules, namely the string black hole with a naked singularity, reduces to a two-dimensional near-singularity geometry. Both of these geometries are described by the two-dimensional low-energy effective action of string theory and are related to each other by scale-factor duality. Secondly, we demonstrate that these near-horizon/singuglarity geometries, including complete α′ corrections, can be described by the two-dimensional Hohm-Zwiebach action. This approach allows for the derivation of non-perturbative and non-singular solutions. Furthermore, the Hohm-Zwiebach action provides a systematic way to investigate the α′-corrected near-horizon/singularity geometries of different kinds of black holes, which are difficult to achieve through the Wess-Zumino-Witten (WZW) model method.

Higher-derivative deformations of the ModMax theory

We present higher-derivative deformations of the ModMax theory which preserve both U(1) duality symmetry and Weyl invariance. In particular, we single out a class of deformations expected to describe a low-energy effective action for the ModMax theory. We also elaborate on (higher-derivative) deformations of the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 super ModMax theory.

Einstein-Grisaru-Zanon gravity

The leading (α′)3-correction to the gravitational low-energy effective action of closed (type II) superstring theory in four-spacetime dimensions defines the Einstein-Grisaru-Zanon gravity action that is applied for a calculation of the leading corrections to the Schwarzschild solution and the Hubble function in the Friedmann-Lemaitre-Robertson-Walker universe, in the first order with respect to the effective string-generated coupling. The solutions found are compared to the corresponding solutions in the Einstein-Bel-Robinson gravity that also modifies the Einstein gravity by the terms quartic in the spacetime curvature. We consider the black hole shadows in the Einstein-Grisaru-Zanon gravity theory and derive the upper bound on the string coupling parameter from the Hawking temperature of a black hole.

The Schwinger-Keldysh coset construction

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.

Probing Gauss-Bonnet-corrected inflation with gravitational waves

The low energy effective action of quantum gravity may include the higher curvature terms such as the Gauss-Bonnet term.The inflaton dynamics may be affected by the Gauss-Bonnet term if there is an inflaton-Gauss-Bonnet coupling.We show that an inflation model with a simple power law potential is made viable if it is coupled to the Gauss-Bonnet term since the prediction on the scalar spectral index and the tensor-to-scalar ratio are modified.We further point out that such a model predicts huge amount of gravitational waves at the high frequency range around 100 GHz–100 THz through the perturbative inflaton decay into gravitons induced by the Gauss-Bonnet term.Thus the spectrum of high frequency gravitational background is a unique feature of the inflation models with a Gauss-Bonnet correction.

Rigid vacua with Brane Supersymmetry Breaking

We construct new string vacua featuring Brane Supersymmetry Breaking, based on T4/ℤN orientifolds with O5+ planes and D5¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ extrm{D}5} $$\\end{document} branes. Differently from the original construction, in these vacua the cancellation of twisted R-R charges of D-branes and orientifold planes is achieved in a non-trivial way, and results in rigid configurations with few open-string moduli, which highly restrict the possible deformations of the model. The breaking of supersymmetry and, consequently, the non-vanishing untwisted and twisted NS-NS tadpoles, generates a rich potential both for the dilaton and the blown-up moduli.We also uncover the stringy origin of the J form entering the gauge kinetic functions in the low-energy effective action, and display its relation to the NS-NS tadpoles for the scalars in the tensor multiplets. As a result, the J form can be consistently identified also when supersymmetry is broken, thus solving an embarrassing puzzle related to its very existence. We also discuss the unitarity constraints for one-dimensional defects in these vacua, where the Kač-Moody algebra for D9 and D5¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ extrm{D}5} $$\\end{document} can be realised both in the left-moving and right-moving sectors.

Non-linear electrodynamics from massive gravity

As a counterpart to the four-fermion interaction, which describes massive vector exchange at low energies, we investigate the low energy effective action of photons under exchange of a massive graviton. We show how integrating out a massive graviton leads to the most general duality-invariant vector interactions in 4D or, vice versa, how any such interactions have a natural interpretation within massive gravity. Moreover, we demonstrate how the special case of Born-Infeld theory arises from arguably the simplest graviton potential within ghost-free dRGT massive gravity.

The connection between nonzero density and spontaneous symmetry breaking for interacting scalars

We consider U(1)-symmetric scalar quantum field theories at zero temperature. At nonzero charge densities, the ground state of these systems is usually assumed to be a superfluid phase, in which the global symmetry is spontaneously broken along with Lorentz boosts and time translations. We show that, in d > 2 spacetime dimensions, this expectation is always realized at one loop for arbitrary non-derivative interactions, confirming that the physically distinct phenomena of nonzero charge density and spontaneous symmetry breaking occur simultaneously in these systems. We quantify this result by deriving universal scaling relations for the symmetry breaking scale as a function of the charge density, at low and high density. Moreover, we show that the critical value of μ above which a nonzero density develops coincides with the pole mass in the unbroken, Poincaré invariant vacuum of the theory. The same conclusions hold non-perturbatively for an O(N) theory with quartic interactions in d = 3 and 4, at leading order in the 1/N expansion. We derive these results by computing analytically the zero-temperature, finite-μ one-loop effective potential, paying special attention to subtle points related to the iε terms. We check our results against the one-loop low-energy effective action for the superfluid phonons in λϕ4 theory in d = 4 previously derived by Joyce and ourselves, which we further generalize to arbitrary potential interactions and arbitrary dimensions. As a byproduct, we find analytically the one-loop scaling dimension of the lightest charge-n operator for the λϕ6 conformal superfluid in d = 3, at leading order in 1/n, reproducing a numerical result of Badel et al. For a λϕ4 superfluid in d = 4, we also reproduce the Lee-Huang-Yang relation and compute relativistic corrections to it. Finally, we discuss possible extensions of our results beyond perturbation theory.

Constraining an Einstein-Maxwell-dilaton-axion black hole at the Galactic Center with the orbit of the S2 star

We derive new constraints on the dilaton parameter appearing in the spherically-symmetric black hole solution of Einstein-Maxwell-dilaton-axion gravity, by studying the geodesic motion of the S2 star in the Galactic Center. Einstein-Maxwell-dilaton-axion black holes represent a compelling alternative to the standard black hole paradigm in General Relativity. This theory emerges from the low energy effective action of the heterotic string theory and has been proven to predict peculiar observational features from the direct imaging of black hole shadows. At a fundamental level, Einstein-Maxwell-dilaton-axion includes additional electromagnetic, dilatonic and axionic fields coupled to the space-time metric. When considering charged non-rotating black hole solutions, the additional fields endow the metric with one extra parameter b, called dilaton parameter, that is theoretically bound to 0 < b < M. Using publicly available astrometric data for S2 we derive an upper bound on b ≲ 12M at 95% confidence level and we demonstrate that only including the measurement of the relativistic orbital precession for S2 is sufficient to reduce this bound to b ≲ 1.4M at the same confidence level. Additionally, using a mock data mimicking future observations of S2 with the GRAVITY interferometer, we show that improved astrometric precision can help further narrow down the allowed dilaton parameter range to b ≲ 0.033M after monitoring the S2 orbit for one and a half period.

Two-dimensional regular string black hole via complete alpha ^{prime } corrections

In string theory, an important challenge is to show if the singularity of black holes can be smoothed out by the complete alpha ^{prime } corrections. The simplest case is to consider a 2D string black hole or 3D black string. This problem was discussed in a gauged Wess–Zumino–Witten (WZW) model and the results are supposed to be correct to all orders in alpha ^{prime } corrections. Based on the recent remarkable progress on classifying all the alpha ^{prime } corrections, in this work, we re-study this problem with the low energy effective spacetime action, and provide classes of exact non-perturbative and non-singular solutions of the 2D black hole/3D black string via complete alpha ^{prime } corrections.

Comments on ABJM free energy on S3 at large N and perturbative expansions in M-theory and string theory

We compare large N expansion of the localization result for the free energy F in the 3d N=6 superconformal U(N)k×U(N)−k Chern-Simons-matter theory to its AdS/CFT counterpart, i.e. to the perturbative expansion of M-theory partition function on AdS×4S7/Zk and to the weak string coupling expansion of type IIA effective action on AdS×4CP3. We show that the general form of the perturbative expansions of F on the two sides of the AdS/CFT duality is indeed the same. Moreover, the transcendentality properties of the coefficients in the large N, large k expansion of F match those in the corresponding M-theory or string theory expansions. To shed light on the structure of the 1-loop M-theory partition function on AdS×4S7/Zk we use the expression for the 1-loop 4-graviton scattering amplitude in the 11d supergravity. We also use the known information about the transcendental coefficients of the leading curvature invariants in the low-energy effective action of type II string theory. Matching of the remaining rational factors in the coefficients requires a precise information about currently unknown RR field strength terms in the corresponding superinvariants.

Palatini variation in generalized geometry and string effective actions

We develop the Palatini formalism within the framework of generalized Riemannian geometry of Courant algebroids. In this context, the Palatini variation of a generalized Einstein–Hilbert–Palatini action - formed using a generalized metric, a Courant algebroid connection (in contrary to the ordinary case, not necessarily a torsionless one) and a volume form - leads naturally to a proper notion of a generalized Levi-Civita connection and low-energy effective actions of string theory.

Slowly rotating and accelerating α′ -corrected black holes in four and higher dimensions

We consider the low-energy effective action of string theory at order $\alpha '$, including $R^2$-corrections to the Einstein-Hilbert gravitational action and non-trivial dilaton coupling. By means of a convenient field redefinition, we manage to express the theory in a frame that enables us to solve its field equations analytically and perturbatively in $\alpha ' $ for a static spherically symmetric ansatz in an arbitrary number of dimensions. The set of solutions we obtain is compatible with asymptotically flat geometries exhibiting a regular event horizon at which the dilaton is well-behaved. For the 4-dimensional case, we also derive the stationary black hole configuration at first order in $\alpha '$ and in the slowly rotating approximation. This yields string theory modifications to the Kerr geometry, including terms of the form $a$, $a^2$, $\alpha '$ and $a\alpha '$. In addition, we obtain the first $\alpha'$ correction to the C-metrics, which accommodates accelerating black holes. We work in the string frame and discuss the connection to the Einstein frame, for which rotating black holes have already been obtained in the literature.

Three dimensional regular black string via loop corrections

It is well known that some spacetime singularities of low energy effective action can be resolved by the effective loop corrections. However, the known potentials for the loop corrections fail to regulate the singularity of three dimensional black string. An alternative method is to introduce an extra flat spatial direction and boost away the singularity by using the O(d, d) rotation with the special Kalb-Ramond field. In this paper, we investigate a new set of non-local dilaton potentials for the effective loop corrections. The result shows that the singularity of three dimensional black string can be consistently resolved by the loop corrections.

Three- and four-point functions in CPT -even Lorentz-violating scalar QED

The renormalization of quantum field theories usually assumes Lorentz and gauge symmetries, besides the general restrictions imposed by unitarity and causality. However, the set of renormalizable theories can be enlarged by relaxing some of these assumptions. In this work, we consider the particular case of a CPT-preserving but Lorentz-breaking extension of scalar QED. For this theory, we calculate the one-loop radiative corrections to the three- and four-point scalar-vector vertex functions, at the lowest order in the Lorentz violation parameters; and we explicitly verify that the resulting low-energy effective action is compatible with the usual gauge invariance requirements. With these results, we complete the one-loop renormalization of the model at the leading order in the Lorentz-violating parameters.

BCF anomaly and higher-group structure in the low energy effective theories of mesons

We discuss the BCF anomaly of massless QCD-like theories, first obtained by Anber and Poppitz, from the viewpoint of the low energy effective theories. We assume that the QCD-like theories exhibit spontaneous chiral symmetry breaking due to a quark bilinear condensate. Using the ’t Hooft anomaly matching condition for the BCF anomaly, we find that the low energy effective action is composed of a chiral Lagrangian and a Wess-Zumino-Witten term together with an interaction term of the η′ meson with the background gauge field for a discrete one-form symmetry. It is shown that the low energy effective action cancels the quantum inconsistencies associated with η′ due to an ambiguity of how to uplift the action to a five-dimensional spacetime with a boundary. The η′ term plays a substantial role in exploring the emergent higher-group structure at low energies.

Anomalies and phases of strongly coupled chiral gauge theories: Recent developments

After many years of investigations, our understanding of the dynamics of strongly coupled chiral gauge theories is still quite unsatisfactory today. Conventional wisdom about strongly coupled gauge theories, successfully applied to QCD, is not always as useful in chiral gauge theories. Recently, some new ideas and techniques have been developed, which involve concepts of generalized symmetries, of gauging a discrete center symmetry, and of generalizing the ’t Hooft anomaly matching constraints to include certain mixed symmetries. This new development has been applied to chiral gauge theories, leading to many interesting, sometimes quite unexpected, results. For instance, in the context of generalized Bars–Yankielowicz and generalized Georgi–Glashow models, these new types of anomalies give a rather clear indication in favor of the dynamical Higgs phase, against confining, flavor symmetric vacua. Another closely related topic is strong anomaly and the effective low-energy action representing it. It turns out that they have significant implications on the phase of chiral gauge theories, giving indications consistent with the findings based on the generalized anomalies. Some striking analogies and contrasts between the massless QCD and chiral gauge theories seem to emerge from these discussions. The aim of this work is to review these developments.

Non-Hermitian quantum system generated from two coupled Sachdev-Ye-Kitaev models

We show that a non-Hermitian two coupled Sachdev-Ye-Kitaev (SYK) model can provide thermodynamic structure equivalent to Hermitian two coupled SYK model. The energy spectrum, the entanglement degree of the ground states and the low energy effective action of this model are not influenced by the non-Hermiticity. The novel biorthogonal ground states demonstrates that two SYK sites, one of which can be in the ground state and the other in the Schwarzian excited state by tuning the non-Hermiticity. We find evidence that the free energy is independent of the non-Hermiticity.