Field Theory Research Articles

Minimal Einstein-Aether theory

We show that there is a phenomenologically and theoretically consistent limit of the generic Einstein-Aether theory in which the Einstein-Aether field equations reduce to Einstein field equations with a perfect fluid distribution sourced by the aether field. This limit is obtained by taking three of the coupling constants of the theory to be zero but keeping the expansion coupling constant to be nonzero. We then consider the further reduction of this limited version of Einstein-Aether theory by taking the expansion of the aether field to be constant (possibly zero), and thereby we introduce the Minimal Einstein-Aether theory that supports the Einstein metrics as solutions with a reduced cosmological constant. The square of the expansion of the unit-timelike aether field shifts the bare cosmological constant and thus provides, via local Lorentz symmetry breaking inherent in the Einstein-Aether theories, a novel mechanism for reconciling the observed, small cosmological constant (or dark energy) with the large theoretical prediction coming from quantum field theories. The crucial point here is that minimal Einstein-Aether theory does not modify the well-tested aspects of General Relativity such as solar system tests and black hole physics including gravitational waves.

Quantum Field Theory of Black Hole Perturbations with Backreaction: I General Framework

In a seminal work, Hawking showed that natural states for free quantum matter fields on classical spacetimes that solve the spherically symmetric vacuum Einstein equations are KMS states of non-vanishing temperature. Although Hawking’s calculation does not include the backreaction of matter on geometry, it is more than plausible that the corresponding Hawking radiation leads to black hole evaporation which is, in principle, observable. Obviously, an improvement of Hawking’s calculation including backreaction is a problem of quantum gravity. Since no commonly accepted quantum field theory of general relativity is available yet, it has been difficult to reliably derive the backreaction effect. An obvious approach is to use the black hole perturbation theory of a Schwarzschild black hole of fixed mass and to quantize those perturbations. However, it is not clear how to reconcile perturbation theory with gauge invariance beyond linear perturbations. In recent work, we proposed a new approach to this problem that applies when the physical situation has an approximate symmetry, such as homogeneity (cosmology), spherical symmetry (Schwarzschild), or axial symmetry (Kerr). The idea, which is surprisingly feasible, is to first construct the non-perturbative physical (reduced) Hamiltonian of the reduced phase space of fully gauge invariant observables and only then apply perturbation theory directly in terms of observables. The task to construct observables is then disentangled from perturbation theory, thus allowing to unambiguously develop perturbation theory to arbitrary orders. In this first paper of the series we outline and showcase this approach for spherical symmetry and second order in the perturbations for Einstein–Klein–Gordon–Maxwell theory. Details and generalizations to other matter and symmetry and higher orders will appear in subsequent companion papers.

T-duality across non-extremal horizons

When applying T-duality to a generic, non-extreme Killing horizon, T-duality is spacelike on one side and timelike on the other. We show, using simple examples from four-dimensional Einstein-Maxwell theory, that the image of the horizon is a singularity which can be understood as an interface between two different T-dual theories and their solutions. Using an embedding into type-II string theory, we show that the singularity occurs when scalars reach the boundary of moduli space, resulting in a breakdown of the effective field theory due to the presence of tensionless strings.

Entanglement islands and the Page curve of Hawking radiation for rotating Kerr black holes

We initiate the study of the information paradox of rotating Kerr black holes by employing the recently proposed island rule. It is known that the scalar field theory near the Kerr black hole horizon can be reduced to the two-dimensional effective theory. Working within the framework of the two-dimensional effective theory and assuming the small angular momentum limit, we demonstrate that the entanglement entropy of Hawking radiation from the nonextremal Kerr black hole follows the Page curve and saturates the Bekenstein-Hawking entropy at late times. In addition, we also discuss the effect of the black hole rotation on the Page time and scrambling time. For the extreme Kerr black hole, the entanglement entropy at late times also approximates the Bekenstein-Hawking entropy of the extreme Kerr black hole. These results imply that entanglement islands can provide a semiclassical resolution of the information paradox for rotating Kerr black holes. Published by the American Physical Society 2024

On Bethe equations of 2d conformal field theory

We study the higher spin algebras of two-dimensional conformal field theory from the perspective of quantum integrability. Starting from Maulik-Okounkov instanton R-matrix and applying the procedure of algebraic Bethe ansatz, we obtain infinite commuting families of Hamiltonians of quantum ILW hierarchy parametrized by the shape of the auxiliary torus. We calculate explicitly the first five of these Hamiltonians. Then, we numerically verify that their joint spectrum can be parametriezed by solutions of Litvinov’s Bethe ansatz equations and we conjecture a general formula for the joint spectrum of all ILW Hamiltonians, based on results of Feigin, Jimbo, Miwa and Mukhin.There are two interesting degeneration limits, the infinitely thick and the infinitely thin auxiliary torus. In one of these limits, the ILW hierarchy degenerates to Yangian or Benjamin-Ono hiearchy and the Bethe equations can be easily solved. The other limit is singular but we can nevertheless extract local Hamiltonians corresponding to quantum KdV or KP hierarchy. Litvinov’s Bethe equations in this local limit provide an alternative to Bethe ansatz equations of Bazhanov, Lukyanov and Zamolodchikov, but are more transparent, work at any rank and are manifestly symmetric under triality symmetry of W\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{W} $$\\end{document}1+∞. Finally, we illustrate analytic properties of the solutions of Bethe equations in minimal models, in particular for Lee-Yang CFT. The analytic structure of Bethe roots is very rich as it captures the representation theory of W\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{W} $$\\end{document}N minimal models.

Exploring interference effects between two ALP effective operators at the LHC

We observe that most studies of axion-like particle (ALP) production channels at the Large Hadron Collider (LHC) focus on a single type of ALP operator for each process in the effective field theory framework. In this work, we propose an alternative approach that considers two or more types of relevant ALP effective operators together in some specific ALP production channels and study their interference effects. Using the pp → tja process with a → γγ as an example, we show that this approach allows us to constrain the ALP interactions with both the W boson and the top quark, as well as their interference in a single process. For the final state with two isolated photons and a top quark decaying semi-leptonically, we predict that the future bounds on the ALP decay constant can reach around fa ~ 10 (20) TeV for 25 GeV < Ma < 100 GeV at the LHC with 300 (3000) fb−1 luminosity.

The linear property of genus-g, n-point, b-boundary, c-crosscap correlation functions in two-dimensional conformal field theory

We propose a method to challenge the calculation of genus-g, bulk n-point, b-boundary, c-crosscap correlation functions with x boundary operators Fg,n,b,cx\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{F}}_{g,n,b,c}^x $$\\end{document} in two-dimensional conformal field theories (CFT2). We show that Fg,n,b,cx\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{F}}_{g,n,b,c}^x $$\\end{document} are infinite linear combinations of genus-g, bulk (n + b + c)-point functions Fg, (n + b + c), and try to obtain the linear coefficients in this work. We show the existence of a single pole structure in the linear coefficients at degenerate limits. A practical method to obtain the infinite linear coefficients is the free field realizations of Ishibashi states. We review the results in Virasoro minimal models M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M} $$\\end{document}(p, p′) and extend it to the N = 1 minimal models SM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{SM} $$\\end{document}(p, p′).

A Goldstone boson equivalence for inflation

The effective field theory of single-field inflation characterizes the inflationary epoch in terms of a pattern of symmetry breaking. An operator acquires a time-dependent vacuum expectation value, defining a preferred spatial slicing. In the absence of dynamical gravity, the fluctuations around the time-dependent background are described by the Goldstone boson associated with this symmetry breaking process. With gravity, the Goldstone is eaten by the metric, becoming the scalar metric fluctuation. In this paper, we will show that in general single-field inflation, the statistics of scalar metric fluctuations are given by the statistics of this Goldstone boson decoupled from gravity up to corrections that are controlled as an expansion in slow-roll parameters. This even holds in the presence of additional parameters, like the speed of sound, that naively enhance the impact of the gravitational terms. In the process, we derive expressions for leading and sub-leading gravitational corrections to all-orders in the Goldstone boson.

Hidden conformal symmetry in AdS2×S2 beyond tree level

Correlators of N=2 hypermultiplets with two-derivative interactions in AdS2×S2 exhibit a hidden four-dimensional conformal symmetry which allows one to repackage all tree-level four-point correlators into a single four-dimensional object corresponding to a contact diagram arising from a massless ϕ4 theory in AdS2×S2. This theory serves as a toy model for IIB string theory in AdS5×S5 and is interesting in its own right because AdS2×S2 describes the near-horizon limit of extremal black holes in four dimensions. We argue that, after acting with an SU(1,1)×SU(2) Casimir, all one-loop correlators can similarly be encoded by a four-dimensional function which arises from a one-loop scalar bubble diagram in AdS2×S2, explaining how the hidden conformal symmetry extends beyond tree level. Finally, we conjecture a scalar effective field theory with a two-derivative interaction in AdS2×S2 whose Witten diagrams should directly reproduce four-point correlators to all loops without acting with Casimirs. Published by the American Physical Society 2024

Normalization of ZZ instanton amplitudes in type 0B minimal superstring theory

Abstract We study ZZ instanton corrections in the (2, 4k) $$ \mathcal{N} $$ N = 1 minimal superstring theory with the type 0B GSO projection, which becomes the type 0B $$ \mathcal{N} $$ N = 1 super-JT gravity in the k → ∞ limit. Each member of the (2, 4k) family of theories has two phases distinguished by the sign of the Liouville bulk cosmological constant. The worldsheet method for computing the one-loop normalization constant multiplying the instanton corrections gives an ill-defined answer in both phases. We fix these divergences using insights from string field theory and find finite, unambiguous results. Each member of the (2, 4k) family of theories is dual to a double-scaled one-matrix integral, where the double-scaling limit can be obtained starting either from a unitary matrix integral with a leading one-cut saddle point, or from a hermitian matrix integral with a leading two-cut saddle point. The matrix integral exhibits a gap-closing transition, which is the same as the double-scaled Gross-Witten-Wadia transition when k = 1. We also compute instanton corrections in the double-scaled matrix integral for all k and in both phases, and find perfect agreement with the string theory results.

Non-universal probes of composite Higgs models: new bounds and prospects for FCC-ee

We study the leading loop-level phenomenology of composite Higgs models via the effective field theory of a strongly interacting light Higgs and top quark (SILH+TQ). We systematically analyze the renormalization group evolution (RGE) of tree-generated operators in the SILH+TQ scenario, finding large mixings of flavor non-universal operators into those affecting electroweak precision observables. We show that these model-independent RG contributions are more important than typical estimates for finite parts. Flavor non-universal effects are completely captured by examining three options for the top mixing: fully composite qL3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {q}_L^3 $$\\end{document}, equal compositeness, and fully composite tR. In the most phenomenologically viable case of a fully composite tR, we show that the strongest bound on the natural parameter space comes from next-to-leading log running of the 4-top operator Ott=t¯RγμtRt¯RγμtR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{O}}_{tt}=\\left({\\overline{t}}_R{\\gamma}_{\\mu }{t}_R\\right)\\left({\\overline{t}}_R{\\gamma}^{\\mu }{t}_R\\right) $$\\end{document} into the Peskin-Takeuchi T parameter. In general, we find that this 2-loop effect allows existing electroweak precision data to give better constraints on 4-top operators than high-energy probes from top production at the LHC. Independent of the top mixing, we find that a future tera-Z machine such as FCC-ee has the potential to probe composite Higgs models up to a scale of m∗ ≳ 25 TeV, and test the naturalness of the electroweak scale at the ≲ 10−4 level.

Pressure-tuned many-body phases through Γ-K valleytronics in moiré bilayer WSe2

Abstract Recent experiments in twisted bilayer transition-metal dichalcogenides have revealed a variety of strongly correlated phenomena. To theoretically explore their origin, we combine here ab initio calculations with correlated model approaches to describe and study many-body effects in twisted bilayer WSe2 under pressure. We find that the interlayer distance is a key factor for the electronic structure, as it tunes the relative energetic positions between the K and the Γ valleys of the valence band maximum of the untwisted bilayer. As a result, applying uniaxial pressure to a twisted bilayer induces a charge-transfer from the K valley to the flat bands in the Γ valley. Upon Wannierizing moiré bands from both valleys, we establish the relevant tight-binding model parameters and calculate the effective interaction strengths using the constrained random phase approximation. With this, we approximate the interacting pressure-doping phase diagram of WSe2 moiré bilayers using self-consistent mean field theory. Our results establish twisted bilayer WSe2 as a platform that allows the direct pressure-tuning of different correlated phases, ranging from Mott insulators, charge-valley-transfer insulators to Kondo lattice-like systems.

Anomalous higher order Ward identities in tensorial group field theories without closure constraint

Abstract The Ward-Takahashi identities are considered as the generalization of the Noether currents available to quantum field theory and include quantum fluctuation effects. Usually, they take the form of relations between correlation functions, which ultimately correspond to the relation between coupling constants of the theory. For this reason, they play a central role in the construction of renormalized theory, providing strong relations between counter-terms. Since last years, they have been intensively considered in the construction of approximate solutions for nonperturbative renormalization group of tensorial group field theories. The construction of these identities is based on the formal invariance of the partition function under a unitary transformation, and Ward’s identities result from a first-order expansion around the identity. Due to the group structure of the transformation under consideration, it is expected that a first-order expansion is indeed sufficient. We show in this article that this does not seem to be the case for a complex tensor theory model, with a kinetic term involving a Laplacian.&amp;#xD;

Torsional Regularization of Self-Energy and Bare Mass of Electron

Abstract In the presence of spacetime torsion, the momentum components do not commute; therefore, in quantum field theory, summation over the momentum eigenvalues will replace integration over the momentum.&amp;#xD;In the Einstein--Cartan theory of gravity, in which torsion is coupled to spin, the separation between the eigenvalues increases with the magnitude of the momentum.&amp;#xD;Consequently, this replacement regularizes divergent integrals in Feynman diagrams with loops by turning them into convergent sums.&amp;#xD;In this article, we apply torsional regularization to the self-energy of a charged lepton in quantum electrodynamics.&amp;#xD;We show that torsion eliminates the ultraviolet divergence of the standard self-energy. &amp;#xD;We also show that the infrared divergence is absent.&amp;#xD;In the end, we calculate the finite bare masses of the electron, muon, and tau lepton: $0.4329\,\mbox{MeV}$, $90.95\,\mbox{MeV}$, and $1543\,\mbox{MeV}$, respectively.&amp;#xD;These values constitute about $85\%$ of the observed, re-normalized masses.

Exactly solvable floquet dynamics for conformal field theories in dimensions greater than two

We find classes of driven conformal field theories (CFT) in d + 1 dimensions with d > 1, whose quench and floquet dynamics can be computed exactly. The setup is suitable for studying periodic drives, consisting of square pulse protocols for which Hamiltonian evolution takes place with different deformations of the original CFT Hamiltonian in successive time intervals. These deformations are realized by specific combinations of conformal generators with a deformation parameter β; the β < 1 (β > 1) Hamiltonians can be unitarily related to the standard (Lüscher-Mack) CFT Hamiltonians. The resulting time evolution can be then calculated by performing appropriate conformal transformations. For d ≤ 3 we show that the transformations can be easily obtained in a quaternion formalism. Evolution with such a single Hamiltonian yields qualitatively different time dependences of observables depending on the value of β, with exponential decays characteristic of heating for β > 1, oscillations for β < 1 and power law decays for β = 1. This manifests itself in the behavior of the fidelity, unequal-time correlator, and the energy density at the end of a single cycle of a square pulse protocol with different hamiltonians in successive time intervals. When the Hamiltonians in a cycle involve generators of a single SU(1, 1) subalgebra we calculate the Floquet Hamiltonian. We show that one can get dynamical phase transitions for any β by varying the time period of a cycle, where the system can go from a non-heating phase which is oscillatory as a function of the time period to a heating phase with an exponentially damped behavior. Our methods can be generalized to other discrete and continuous protocols. We also point out that our results are expected to hold for a broader class of QFTs that possesses an SL(2, C) symmetry with fields that transform as quasi-primaries under this. As an example, we briefly comment on celestial CFTs in this context.

Proof of 5D An AGT conjecture at β = 1

In this paper, we give a proof of 5D An AGT conjecture at β = 1, where the gauge theory side is one dimension higher than the original 4D case, and corresponds to the q-deformation of the 2D conformal field theory side. We define a q-deformed An Selberg integral, which generalizes the An Selberg integral and the q-deformed A1 Selberg integral in the literature. A q-deformed An Selberg average formula with n + 1 Schur polynomials is proposed and proved to complete the proof.

Quantum Liquids: Emergent Higher-Rank Gauge Theory and Fractons

Fractons emerge from many-body systems, featuring subdimensional particles with restricted mobility. These particles have attracted interest for their roles across disciplines, including topological quantum codes, quantum field theory, emergent gravity, and quantum information. They display unique nonequilibrium behaviors such as nonergodicity and glassy dynamics. This review offers a structured overview of fracton phenomena, especially those of gapless fracton liquids, which enable collective modes similar to gauge fluctuations in Maxwell's electromagnetic framework, yet their phenomena are distinguished by a unique conservation law that restricts the mobility of individual charges and monopoles. We delve into the theoretical basis of three-dimensional (3D) fracton liquids, exploring emergent symmetric tensor gauge theories and their properties. We also discuss the material realization of fracton liquids in Yb-based pyrochlore lattices and other synthetic quantum matter platforms.

Topological photon, spin, and Euclidean group E(2)

The proposition that photon is a topological object [S. C. Tiwari, J. Math. Phys. 49, 032303 (2008)] is given rigorous foundation based on pure vector field theory independent of the electromagnetic fields. Holomorphy of 4-dimensional spacetime and the nature of topological obstructions are investigated to articulate singular vortex model for photon. The utility of the Euclidean symmetry group is discussed in detail for the proposed photon model.

Revisiting the fermion-field nontopological solitons

Nontopological fermionic solitons exist across a diverse range of particle physics models and have rich cosmological implications. This study establishes a general framework for calculating fermionic soliton profiles under arbitrary scalar potentials, utilizing relativistic mean field theory to accurately depict the interaction between the fermion condensate and the background scalar field. Within this framework, the conventional “fermion bound states” are revealed as a subset of fermionic solitons. In addition, we demonstrate how the analytical formulae in previous studies are derived as special cases of our algorithm, discussing the validity of such approximations. Furthermore, we explore the phenomenology of fermionic solitons, highlighting new formation mechanisms and evolution paths, and reconsidering the possibility of collapse into primordial black holes.

Energy growth in VLVL→ VLVL, VLVLh scattering to probe Higgs cubic and HEFT interactions

We compute the energy scales of perturbative unitarity violation in VLVL → VLVLh processes and compare them to VLVL → hhh process, where VL refers to a longitudinal mode of Z or W boson, and h the Higgs boson. Using these energy scales, we determine which process is more sensitive to potential modifications in the Higgs sector at high-energy colliders. Within the Higgs Effective Field Theory (HEFT), we consider the Higgs cubic coupling and other interactions with and without derivatives. Any HEFT interactions predict the perturbative unitarity violation at a finite scale, and in a generic case, the minimalistic process is 2 → 3 scattering. Our analysis reveals that the energy scales for unitarity violation in VLVL → VLVLh and VLVL → hhh processes are similar across all scenarios considered. If the backgrounds are similar, VLVLh final states are more feasible because VLVLh has higher branching ratios in cleaner decay modes than hhh. We also investigate HEFT derivative interactions derived from various UV models. In these cases, both VLVL → VLVL and VLVL → hh processes exhibit unitarity violating behavior. We demonstrate that the energy scales for unitarity violation in VLVL final states are comparable to or even lower than those in the hh final state.