Field Theory Research Articles

Tensor renormalization group for fermions.

We review the basic ideas of the tensor renormalization group method and show how they can be applied for lattice field theory models involving relativistic fermions and Grassmann variables in arbitrary dimensions. We discuss recent progress for entanglement filtering, loop optimization, bond-weighting techniques and matrix product decompositions for Grassmann tensor networks. The new methods are tested with two-dimensional Wilson-Majorana fermions and multi-flavor Gross-Neveu models. We show that the methods can also be applied to the fermionic Hubbard model in 1+1 and 2+1 dimensions.

Anomalous dispersion, superluminality, and instabilities in two-flavor theories with local non-Hermitian mass mixing

Pseudo-Hermitian field theories possess a global continuous “similarity” symmetry, interconnecting the theories with the same physical particle content and an identical mass spectrum. In their regimes with real spectra, within this family of similarity transformations, there is a map from the non-Hermitian theory to its Hermitian similarity partner. We promote the similarity transformation to a local symmetry, which requires the introduction of a new vector similarity field as a connection in the similarity space of non-Hermitian theories. In the case of non-Hermitian two-flavor scalar or fermion mixing and by virtue of a novel IR/UV mixing effect, the effect of inhomogeneous non-Hermiticity then reveals itself via anomalous dispersion, instabilities, and superluminal group velocities at very high momenta, thus setting an upper bound on the particle momentum propagating through inhomogeneous backgrounds characterized by Lagrangians with non-Hermitian mass matrices. Such a non-Hermitian extension of the Standard Model of particle physics, encoded in a weak inhomogeneity of the non-Hermitian part of the fermion mass matrix, may nevertheless provide us with a low-energy particle spectrum consistent with experimentally observed properties. Published by the American Physical Society 2024

Topology of Born–Infeld-AdS black hole phase transitions: Bulk and CFT sides

The thermodynamic criticality of the AdS black holes serves as an important structure during the thermal phase transition. This paper discusses about the critical points and their topology during thermal phase transitions of the Born–Infeld AdS black holes. We make such investigations using two different topological approaches, namely, using Duan’s topological current ϕ-mapping theory, and the off-shell free energy. Within Duan’s formalism, we observe that for a given value of the Born–Infeld parameter b, there exists an associated electric charge parameter Q, which is highly sensitive to the topological phase transitions. This way we examine the connections of the first-order phase transition and the topological nature of the critical points. We find that the topological nature has a possible breakdown in certain parametric ranges. In effect, we determine the unconventional and the conventional phase critical points as the creation (topologically vortex) and annihilation (topologically anti-vortex) points (pairs). As the second approach, we call the off-shell free energy to determine the topological classes: of which one corresponds to the AdS-Schwarzschild black hole phases, while the other provides a possible topological phase transition. Here we also reveal a novel phase transition between two unstable phases, namely, the unstable small black hole and the intermediate black holes. For certain parametric values of the Born–Infeld parameter and the pressure, we also study the different topological descriptions that inevitably correspond to the AdS-Reissner–Nordström black hole phases. As a consistency check of the critical points during the topological phase transitions, we study the vortex/anti-vortex annihilation thermodynamics from local as well as global thermodynamic viewpoints. At the end, a special emphasis has been put on phase transition from the conformal field theory perspective revealing that the Born–Infeld-AdS black hole and its dual CFT share identical topology. Consequently, any topological transition that occurs in the bulk corresponds to a parallel transition in the dual CFT.

Universal fine grained asymptotics of free and weakly coupled quantum field theory

We give a rigorous proof that in any free quantum field theory with a finite group global symmetry G, on a compact spatial manifold, at sufficiently high energy, the density of states ρα(E) for each irreducible representation α of G obeys a universal formula as conjectured by Harlow and Ooguri. We further prove that this continues to hold in a weakly coupled quantum field theory, given an appropriate scaling of the coupling with temperature. This generalizes similar results that were previously obtained in (1 + 1)-D to higher spacetime dimension. We discuss the role of averaging in the density of states, and we compare and contrast with the case of continuous group G, where we prove a universal, albeit different, behavior.

Emergent symmetries at criticality in multi field RFT/DP

We study multifield extensions of Reggeon Field Theory (also equivalent to Directed Percolation model) at criticality in the perturbative ϵ-expansion below the upper critical dimension Dc = 4 at one loop, for the special case when all fields have the same scale (anomalous) dimensions. Analyzing all the fixed points of the renormalization group flow for N = 2 flavors and some for N = 3, we find scale invariant solutions which are characterized by specific emergent global symmetries of the interacting potential. We also study two infinite families as a function of N having ℤN and SN+1 symmetries.

Engineering holography with stabilizer graph codes

The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the experimental realization of such holographic codes now within reach. Formulating the hyperbolic pentagon code in terms of a stabilizer graph code, we give gate sequences that are tailored to systems with long-range interactions. We show how to obtain encoding and decoding circuits for the hyperbolic pentagon code, before focusing on a small instance of the holographic code on twelve qubits. Our approach allows to verify holographic properties by partial decoding operations, recovering bulk degrees of freedom from their nearby boundary.

Non-minimal coupling, negative null energy, and effective field theory

The non-minimal coupling of scalar fields to gravity has been claimed to violate energy conditions, leading to exotic phenomena such as traversable wormholes, even in classical theories. In this work we adopt the view that the non-minimal coupling can be viewed as part of an effective field theory (EFT) in which the field value is controlled by the theory’s cutoff. Under this assumption, the average null energy condition, whose violation is necessary to allow traversable wormholes, is obeyed both classically and in the context of quantum field theory. In addition, we establish a type of "smeared" null energy condition in the non-minimally coupled theory, showing that the null energy averaged over a region of spacetime obeys a state dependent bound, in that it depends on the allowed field range. We finally motivate our EFT assumption by considering when the gravity plus matter path integral remains semi-classically controlled.

Fuzzy onionlike space as a matrix model

We propose a matrix model realization of a three-dimensional quantum space. It has an onionlike structure composed of concentric fuzzy spheres of increasing radius. The angular part of the Laplace operator is inherited from that of the fuzzy sphere. The radial part is constructed using operators that relate matrices of various sizes using the matrix harmonic expansion. As an example of this approach, we produce a numerical simulation of a scalar quantum field theory, the classical heat transfer, study the quantum-mechanical hydrogen atom, and consider some analytical aspects of the scalar field theory on this space. Published by the American Physical Society 2024

Monopoles in Dirac spin liquids and their symmetries from instanton calculus

The Dirac spin liquid (DSL) is a two-dimensional (2D) fractionalized Mott insulator featuring massless Dirac spinon excitations coupled to a compact U(1) gauge field, which allows for flux-tunneling instanton events described by magnetic monopoles in (2+1)D Euclidean spacetime. The state-operator correspondence of conformal field theory has been used recently to define associated monopole operators and determine their quantum numbers, which encode the microscopic symmetries of conventional ordered phases proximate to the DSL. In this work, we utilize semiclassical instanton methods not relying on conformal invariance to construct monopole operators directly in (2+1)D spacetime as instanton-induced ’t Hooft vertices, i.e., fermion-number-violating effective interactions originating from zero modes of the Euclidean Dirac operator in an instanton background. In the presence of a flavor-adjoint fermion mass, resummation of the instanton gas is shown to select the correct monopole to be proliferated, in accordance with predictions of the state-operator correspondence. We also show that our instanton-based approach is able to determine monopole quantum numbers on bipartite lattices.

Complexity in tame quantum theories

Inspired by the notion that physical systems can contain only a finite amount of information or complexity, we introduce a framework that allows for quantifying the amount of logical information needed to specify a function or set. We then apply this methodology to a variety of physical systems and derive the complexity of parameter-dependent physical observables and coupling functions appearing in effective Lagrangians. In order to implement these ideas, it is essential to consider physical theories that can be defined in an o-minimal structure. O-minimality, a concept from mathematical logic, encapsulates a tameness principle. It was recently argued that this property is inherent to many known quantum field theories and is linked to the UV completion of the theory. To assign a complexity to each statement in these theories one has to further constrain the allowed o-minimal structures. To exemplify this, we show that many physical systems can be formulated using Pfaffian o-minimal structures, which have a well-established notion of complexity. More generally, we propose adopting sharply o-minimal structures, recently introduced by Binyamini and Novikov, as an overarching framework to measure complexity in quantum theories.

Thermal entanglement in conformal junctions

We consider a quantum junction described by a 1+1-dimensional boundary conformal field theory (BCFT). Our analysis focuses on correlations emerging at finite temperature, achieved through the computation of entanglement measures. Our approach relies on characterizing correlation functions of twist fields using BCFT techniques. We provide non-perturbative predictions for the crossover between low and high temperatures. An intriguing interplay between bulk and boundary effects, associated with the bulk/boundary scaling dimensions of the fields above, is found. In particular, the entanglement entropy is primarily influenced by bulk thermal fluctuations, exhibiting extensiveness for large system sizes with a prefactor independent of the scattering properties of the defect. In contrast, negativity is governed by fluctuations across the entangling points only, adhering to an area law; its value depends non-trivially on the defect, and it diverges logarithmically as the temperature is decreased. To validate our predictions, we numerically check them for free fermions on the lattice, finding good agreement.

Universal Pattern in Quantum Gravity at Infinite Distance.

Quantum gravitational effects become significant at a cutoff that can be much lower than the Planck scale whenever there is a large number of light fields. This is expected to occur at any perturbative limit of an effective field theory coupled to gravity, or equivalently, at infinite distance in the field space of the UV completion. In this note, we present a universal pattern that links the asymptotic variation in field space of the quantum gravity cutoff Λ_{sp} and the characteristic mass of the lightest tower of states m: (∇[over →]m/m)·(∇[over →]Λ_{sp}/Λ_{sp})=[1/(d-2)], with d the spacetime dimension. This restriction can be used to make more precise several Swampland criteria that constrain any effective field theory which can be consistently coupled to quantum gravity.

On democratic string field theories

We reexamine democratic open string field theories, namely, theories in which string fields are not constrained to a single picture number and picture changing is obtained as a gauge transformation. We describe several possibilities for regular free theories and attempt to construct the lowest order interaction term and identify the lowest order gauge transformation for some of these theories. We also discuss projections over string field spaces that might be needed for a consistent off-shell implementation of picture changing.

Efficient Modeling of High-Generation Dendrimers in Solution Using Dynamical Self-Consistent Field Theory

Efficient Modeling of High-Generation Dendrimers in Solution Using Dynamical Self-Consistent Field Theory

Multi-Higgs boson signals of a modified muon Yukawa coupling at a muon collider

We study di-Higgs and tri-Higgs boson productions at a muon collider as functions of the modification of the muon Yukawa coupling resulting from new physics parametrized by the dimension-six mass operator. We show that the di-Higgs signal can be used to observe a deviation in the muon Yukawa coupling at the 10% level for s=10 TeV and at the 3.5% level for s=30 TeV. The tri-Higgs signal improves the sensitivity dramatically with increasing s, reaching 0.8% at s=30 TeV. We also study all processes involving Goldstone bosons originating from the same operator, discuss possible model dependence resulting from other operators of dimension-six and higher, and identify μ+μ−→hh, μ+μ−→hhh, and μ+μ−→hZLZL as golden channels. We further extend the study to an effective field theory including two Higgs doublets with type-II couplings and show that di-Higgs and tri-Higgs signals involving heavy Higgs bosons can be enhanced in the alignment limit by a factor of (tanβ)4 and (tanβ)6, respectively, which results in the potential sensitivity to a modified muon Yukawa coupling at the 10−6 level already at a s=10 TeV muon collider. The results can easily be customized for other extensions of the Higgs sector. Published by the American Physical Society 2024

Bosonic rational conformal field theories in small genera, chiral fermionization, and symmetry/subalgebra duality

A (1 + 1)D unitary bosonic rational conformal field theory (RCFT) may be organized according to its genus, a tuple (c,C) consisting of its central charge c and a unitary modular tensor category C which describes the (2 + 1)D topological quantum field theory for which its maximally extended chiral algebra forms a holomorphic boundary condition. We establish a number of results pertaining to RCFTs in “small” genera, by which we informally mean genera with the central charge c and the number of primary operators rank(C) both not too large. We start by completely solving the modular bootstrap problem for theories with at most four primary operators. In particular, we characterize, and provide an algorithm which efficiently computes, the function spaces to which the partition function of any bosonic RCFT with rank(C)≤4 must belong. Using this result, and leveraging relationships between RCFTs and holomorphic vertex operator algebras which come from “gluing” and cosets, we rigorously enumerate all bosonic theories in 95 of the 105 genera (c,C) with c ≤ 24 and rank(C)≤4. This includes as (new) special cases the classification of chiral algebras with three primaries and c < 120/7 ∼ 17.14, and the classification of chiral algebras with four primaries and c < 62/3 ∼ 20.67. We then study two applications of our classification. First, by making use of chiral versions of bosonization and fermionization, we obtain the complete list of purely left-moving fermionic RCFTs with c < 23 as a corollary of the results of the previous paragraph. Second, using a (conjectural) concept which we call “symmetry/subalgebra duality,” we precisely relate our bosonic classification to the problem of determining certain generalized global symmetries of holomorphic vertex operator algebras.

Hierarchy of curvatures in exceptional geometry

Despite remarkable success in describing supergravity reductions and backgrounds, generalized geometry and exceptional field theory are still lacking a fundamental object of differential geometry, the Riemann tensor. We show that to construct it, a hierarchy of connections is required. They complement the spin connection with higher representations known from the tensor hierarchy. This approach allows to define generalized homogeneous spaces which underlie generalized U-duality, admit consistent truncations and provide a huge class of new flux backgrounds with nontrivial structure groups. Published by the American Physical Society 2024

Analysis of BOSS galaxy data with weighted skew-spectra

We present the first application of the weighted skew-spectra to analyze non-Gaussian information in galaxy survey data. Using the tree-level galaxy skew-spectra together with the one-loop power spectrum multipoles, we analyze the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) galaxy clustering data, and target our search towards the equilateral bispectrum shape of primordial non-Gaussianity. We use the Effective Field Theory model for the galaxy power spectrum and bispectrum, and account for systematic effects, such as the survey geometry. From our likelihood analysis, we find f NL equil = -34+296 -334 at 68% CL, consistent with previous works, while systematic errors from our treatment of the survey geometry lead to an unreliable estimation of f NL ortho. We further constrain the bias and counterterm parameters, while keeping the cosmology fixed to Planck 2018 values. As a check, we also validate our analysis pipeline using the Nseries simulation suite.

The BOSS bispectrum analysis at one loop from the Effective Field Theory of Large-Scale Structure

We analyze the BOSS power spectrum monopole and quadrupole, and the bispectrum monopole and quadrupole data, using the predictions from the Effective Field Theory of Large-Scale Structure (EFTofLSS). Specifically, we use the one loop prediction for the power spectrum and the bispectrum monopole, and the tree level for the bispectrum quadrupole. After validating our pipeline against numerical simulations as well as checking for several internal consistencies, we apply it to the observational data. We find that analyzing the bispectrum monopole to higher wavenumbers thanks to the one-loop prediction, as well as the addition of the tree-level quadrupole, significantly reduces the error bars with respect to our original analysis of the power spectrum at one loop and bispectrum monopole at tree level. After fixing the spectral tilt to Planck preferred value and using a Big Bang Nucleosynthesis prior, we measure σ 8 = 0.794 ± 0.037, h = 0.692 ± 0.011, and Ω m = 0.311 ± 0.010 to about 4.7%, 1.6%, and 3.2%, at 68% CL, respectively.This represents an error bar reduction with respect to the power spectrum-only analysis of about 30%, 18%, and 13% respectively. Remarkably, the results are compatible with the ones obtained with a power-spectrum-only analysis, showing the power of the EFTofLSS in simultaneously predicting several observables. We find no tension with Planck.

Gravitational redshift constraints on the effective theory of interacting dark energy

Upcoming galaxy surveys provide the necessary sensitivity to measure gravitational redshift, a general relativistic effect that generates a dipole in galaxy clustering data when correlating two distinct populations of galaxies. Here, we study the constraining power of gravitational redshift within the framework of the effective theory of interacting dark energy. This formalism describes linear cosmological perturbations in scalar-tensor theories of gravity with a limited number of free functions, and allows each particle species to be coupled differently to the gravitational sector. In this work, we focus on Horndeski theories with a non-minimal coupling of dark matter to the scalar degree of freedom, yielding a breaking of the weak equivalence principle for this cosmic component, a scenario that is yet untested. We show that the dipole generated by gravitational redshift significantly breaks degeneracies and tightens the constraints on the parameters of the effective theory compared to the standard redshift-space distortion analysis solely based on the even multipoles in the galaxy correlation function, with an improvement of up to ∼ 50% for populations with a galaxy bias difference equal to 1. We make the Python package EF-TIGRE (Effective Field Theory of Interacting dark energy with Gravitational REdshift) developed for this work publicly available (https://github.com/Mik3M4n/EF-TIGRE).