Quantum Field Theory Research Articles

Unambiguous discrimination of general quantum operations.

The discrimination of quantum operations has long been an intriguing challenge, with theoretical research notably advancing our understanding of the quantum features in discriminating quantum objects. This challenge is closely related to the discrimination of quantum states, and proof-of-principle demonstrations of the latter have already been realized using optical photons. However, the experimental demonstration of discriminating general quantum operations, including both unitary and nonunitary operations, has remained elusive. In general quantum systems, especially those with high dimensions, the preparation of arbitrary quantum states and the implementation of arbitrary quantum operations and generalized measurements are nontrivial tasks. Here, we experimentally demonstrate the optimal unambiguous discrimination of up to six displacement operators and the unambiguous discrimination of nonunitary quantum operations. Our results demonstrate powerful tools for experimental research in quantum information processing and are expected to stimulate a wide range of valuable applications in the field of quantum sensing.

Soft-photon theorem for pion-proton elastic scattering revisited

We discuss the reactions πp→πp and πp→πpγ from a general quantum field theory (QFT) point of view, describing these reactions in QCD and lowest relevant order of electromagnetism. We consider the pion-proton elastic scattering both off shell and on shell. The on-shell amplitudes for π±p→π±p scattering are described by two invariant amplitudes, while the off-shell amplitudes contain eight invariant amplitudes. We study the photon emission amplitudes in the soft-photon limit where the center-of-mass photon energy ω→0. The Laurent expansion in ω of the π±p→π±pγ amplitudes is considered and the terms of the orders ω−1 and ω0 are derived. These terms can be expressed by the on-shell invariant amplitudes and their partial derivatives with respect to s and t. The pole term ∝ω−1 in the amplitudes corresponds to Weinberg’s soft-photon theorem and is well known from the literature. We derive the next-to-leading term ∝ω0 using only rigorous methods of QFT. We give the relation of the Laurent series for π0p→π0pγ and Low’s soft-photon theorem. Our formulas for the amplitudes in the limit ω→0 are valid for photon momentum k satisfying k2≥0, k0=ω≥0, that is, for both real and virtual photons. Here we consider a limit where with ω→0 we have also k2→0. We discuss the behavior of the corresponding cross sections for π−p→π−pγ with respect to ω for ω→0. We consider cross sections for unpolarized as well as polarized protons in the initial and final states. Published by the American Physical Society 2024

New purely damped pairs of quasinormal modes in a hot and dense strongly-coupled plasma

Abstract Perturbed black holes exhibit damped oscillations whose eigenfrequencies define their quasinormal modes (QNMs). In the case of asymptotically Anti-de Sitter (AdS) black holes, the spectra of QNMs are related to the near-equilibrium behavior of specific strongly interacting quantum field theories via the holographic gauge-gravity duality. In the present work, we numerically obtain the spectra of homogeneous non-hydrodynamic QNMs of a top-down holographic construction called the 2 R-Charge Black Hole (2RCBH) model, which describes a hot and dense strongly-coupled plasma. The main result is the discovery of a new structure of pairs of purely imaginary QNMs. Those new purely damped QNMs dominate the late time equilibration of the strongly-coupled plasma at large values of the chemical potential, while at lower values the fundamental QNMs are instead ordinary poles with imaginary and real parts describing oscillatory decaying perturbations. We also observe a new phenomenon of asymptotic pole fusion for different pairs of purely imaginary QNMs at asymptotically large values of the chemical potential. This phenomenon corresponds to the asymptotic merging of the two poles within each pair of purely imaginary QNMs, with the different pairs of merged poles being evenly spaced by a constant value of 4π in all the different perturbation channels associated to different irreducible representations of the spatial SO(3) rotation symmetry of the medium. In particular, this indicates that characteristic equilibration times for the plasma develop upper bounds that cannot be surpassed by further doping the medium with increasing values of the chemical potential.

Neutrino oscillation in the presence of background classical sources

Abstract The presence of background classical sources affects a quantum field theory significantly in different ways. Neutrino oscillation is a phenomenon that confirms that neutrinos are massive fermions in nature, a celebrated result in modern physics. Neutrino oscillation plays an important role in many astrophysical observations. However, the interactions between the background classical sources with neutrinos are not often considered. In the present article, we show the effect of some classical sources, namely matter currents, electromagnetic waves, torsion, and gravitational waves on neutrino oscillation. It is shown explicitly that the above sources can change the helicity state of neutrinos during neutrino oscillation.

Schwinger vs Coleman: Magnetic charge renormalization

Abstract The kinetic mixing of two U(1) gauge theories can result in a massless photon that has perturbative couplings to both electric and magnetic charges. This framework can be used to perturbatively calculate in a quantum field theory with both kinds of charge. Here we reexamine the running of the magnetic charge, where the calculations of Schwinger and Coleman sharply disagree. We calculate the running of both electric and magnetic couplings and show that the disagreement between Schwinger and Coleman is due to an incomplete summation of topological terms in the perturbation series. We present a momentum space prescription for calculating the loop corrections in which the topological terms can be systematically separated for resummation. Somewhat in the spirit of modern amplitude methods we avoid using a vector potential and use the field strength itself, thereby trading gauge redundancy for the geometric redundancy of Stokes surfaces. The resulting running of the couplings demonstrates that Dirac charge quantization is independent of renormalization scale, as Coleman predicted. As a simple application we also bound the parameter space of magnetically charged states through the experimental measurement of the running of electromagnetic coupling.

Robustness of quantum correlation in quantum energy teleportation

In this article, we explore a feedback-control protocol in different quantum field theories (QFTs) to study the quantum correlation in nonunitary evolution of quantum systems. Traditional studies on QFTs focus on quantum entanglement of pure states under the unitary evolution, however, we examine quantum correlation in mixed states using quantum energy teleportation (QET), which is an energy transfer protocol by utilizing ground state entanglement, and introduce quantum discord as a measure. QET involves a midcircuit measurement, which disrupts pure state entanglement. Despite this, our analysis demonstrates that quantum discord maintains the correlation throughout the QET process. We conducted numerical analyses with benchmark models including the Nambu-Jona-Lasinio (NJL) model, revealing that quantum discord consistently acts as an order parameter for phase transitions. The model is extended in a way that it has both the chiral chemical potential and the chemical potential, which are useful to study the phase structures mimicking the chiral imbalance between left- and right- quarks coupled to the chirality density operator. In all cases we studied, the quantum discord behaved as an order parameter of the phase transition. Published by the American Physical Society 2024

Trace anomalies and the graviton-dilaton amplitude

Abstract We consider 3+1 dimensional Quantum Field Theories (QFTs) coupled to the dilaton and the graviton. We show that the graviton-dilaton scattering amplitude receives a universal contribution which is helicity flipping and is proportional to ∆c − ∆a along any RG flow, where ∆c and ∆a are the differences of the UV and IR c- and a-trace anomalies respectively. This allows us to relate ∆c − ∆a to spinning massive states in the spectrum of the QFT. We test our predictions in two simple examples: in the theory of a massive free scalar and in the theory of a massive Dirac fermion (a more complicated example is provided in a companion paper [1]). We discuss possible applications.

Anomalies of non-invertible symmetries in (3+1)d

Anomalies of global symmetries are important tools for understanding the dynamics of quantum systems. We investigate anomalies of non-invertible symmetries in 3+1d using 4+1d bulk topological quantum field theories given by Abelian two-form gauge theories, with a 0-form permutation symmetry. Gauging the 0-form symmetry gives the 4+1d “inflow” symmetry topological field theory for the non-invertible symmetry. We find a two levels of anomalies: (1) the bulk may fail to have an appropriate set of loop excitations which can condense to trivialize the boundary dynamics, and (2) the “Frobenius-Schur indicator” of the non-invertible symmetry (generalizing the Frobenius-Schur indicator of 1+1d fusion categories) may be incompatible with trivial boundary dynamics. As a consequence we derive conditions for non-invertible symmetries in 3+1d to be compatible with symmetric gapped phases, and invertible gapped phases. Along the way, we see that the defects characterizing \mathbb{Z}_{4}ℤ4 ordinary symmetry host worldvolume theories with time-reversal symmetry \mathsf{T}𝖳 obeying the algebra \mathsf{T}^{2}=C𝖳2=C or \mathsf{T}^{2}=(-1)^{F}C,𝖳2=(−1)FC, with CC a unitary charge conjugation symmetry. We classify the anomalies of this symmetry algebra in 2+1d and further use these ideas to construct 2+1d topological orders with non-invertible time-reversal symmetry that permutes anyons. As a concrete realization of our general discussion, we construct new lattice Hamiltonian models in 3+1d with non-invertible symmetry, and constrain their dynamics.

Supergeometric quantum effective action

Supergeometric quantum field theories (SG-QFTs) are theories that go beyond the standard supersymmetric framework, since they allow for general scalar-fermion field transformations on the configuration space of a supermanifold, without requiring an equality between bosonic and fermionic degrees of freedom. After revisiting previous considerations, we extend them by calculating the one-loop effective action of minimal SG-QFTs that feature nonzero fermionic curvature in two and four spacetime dimensions. By employing an intuitive approach to the Schwinger–DeWitt heat-kernel technique and a novel field-space generalized Clifford algebra, we derive the ultraviolet structure of characteristic effective-field-theory (EFT) operators up to four spacetime derivatives that emerge at the one-loop order and are of physical interest. Upon minimizing the impact of potential ambiguities due to the so-called multiplicative anomalies, we find that the EFT interactions resulting from the one-loop supergeometric effective action are manifestly diffeomorphically invariant in configuration space. The extension of our approach to evaluating higher loops of the supergeometric quantum effective action is described. The emerging landscape of theoretical and phenomenological directions for further research of SG-QFTs is discussed. Published by the American Physical Society 2024

On the role of fiducial structures in minisuperspace reduction and quantum fluctuations in LQC

Abstract In spatially non-compact homogeneous minisuperpace models, spatial integrals in the Hamiltonian and symplectic form must be regularised by confining them to a finite volume Vo , known as the fiducial cell. As this restriction is unnecessary in the complete field theory before homogeneous reduction, the physical significance of the fiducial cell has been largely debated, especially in the context of (loop) quantum cosmology. Understanding the role of Vo is in turn essential for assessing the minisuperspace description’s validity and its connection to the full theory. In this work we present a systematic procedure for the field theory reduction to spatially homogeneous and isotropic minisuperspaces within the canonical framework and apply it to both a massive scalar field theory and gravity. Our strategy consists in implementing spatial homogeneity via second-class constraints for the discrete field modes over a partitioning of the spatial slice into countably many disjoint cells. The reduced theory’s canonical structure is then given by the corresponding Dirac bracket. Importantly, the latter can only be defined on a finite number of cells homogeneously patched together. This identifies a finite region, the fiducial cell, whose physical size acquires then a precise meaning already at the classical level as the scale over which homogeneity is imposed. Additionally, the procedure allows us to track the information lost during homogeneous reduction and how the error depends on Vo . We then move to the quantisation of the classically reduced theories, focusing in particular on the relation between the theories for different Vo , and study the implications for statistical moments, quantum fluctuations, and semiclassical states. In the case of a quantum scalar field, a subsector of the full quantum field theory where the results from the ‘first reduced, then quantised’ approach can be reproduced is identified and the conditions for this to be a good approximation are also determined.

Crossing symmetry and the crossing map

We introduce and study the crossing map, a closed linear map acting on operators on the tensor square of a given Hilbert space that is inspired by the crossing property of quantum field theory. This map turns out to be closely connected to Tomita–Takesaki modular theory. In particular, crossing symmetric operators, namely those operators that are mapped to their adjoints by the crossing map, define endomorphisms of standard subspaces. Conversely, such endomorphisms can be integrated to crossing symmetric operators. We also investigate the relation between crossing symmetry and natural compatibility conditions with respect to unitary representations of certain symmetry groups, and furthermore introduce a generalized crossing map defined by a real object in an abstract [Formula: see text]-tensor category, not necessarily consisting of Hilbert spaces and linear maps. This latter crossing map turns out to be closely related to the (unshaded, finite-index) subfactor theoretical Fourier transform. Lastly, we provide families of solutions of the crossing symmetry equation, solving in addition the categorical Yang–Baxter equation, associated with an arbitrary Q-system.

Some Exact Green Function Solutions for Non-Linear Classical Field Theories

We consider some non-linear non-homogeneous partial differential equations (PDEs) and derive their exact Green function solution as a functional Taylor expansion in powers of the source. The kind of PDEs we consider are dispersive ones where the exact solution of the corresponding homogeneous equations can have some known shape. The technique has a formal similarity with the Dyson–Schwinger set of equations to solve quantum field theories. However, there are no physical constraints. Indeed, we show that a complete coincidence with the statistical field model of a quartic scalar theory can be achieved in the Gaussian expansion of the cumulants of the partition function.

Noninvertible Symmetries Act Locally by Quantum Operations

of quantum field theories and many-body systems generalize the concept of symmetries by allowing noninvertible operations in addition to more ordinary invertible ones described by groups. The aim of this Letter is to point out that these noninvertible symmetries act on local operators by , i.e., completely positive maps between density matrices, which form a natural class of operations containing both unitary evolutions and measurements and play an important role in quantum information theory. This observation will be illustrated by the Kramers-Wannier duality of the one-dimensional quantum Ising chain, which is a prototypical example of noninvertible symmetry operations. Published by the American Physical Society 2024

Fermionic integrable models and graded Borchers triples

We provide an operator-algebraic construction of integrable models of quantum field theory on 1+1-dimensional Minkowski space with fermionic scattering states. These are obtained by a grading of the wedge-local fields or, alternatively, of the underlying Borchers triple defining the theory. This leads to a net of graded-local field algebras, of which the even part can be considered observable, although it is lacking Haag duality. Importantly, the nuclearity condition implying nontriviality of the local field algebras is independent of the grading, so that existing results on this technical question can be utilized. Application of Haag–Ruelle scattering theory confirms that the asymptotic particles are indeed fermionic. We also discuss connections with the form factor programme.

Generalized symmetries in 2D from string theory: SymTFTs, intrinsic relativeness, and anomalies of non-invertible symmetries

Abstract Generalized global symmetries, in particular non-invertible and categorical symmetries, have become a focal point in the recent study of quantum field theory (QFT). In this paper, we investigate aspects of symmetry topological field theories (SymTFTs) and anomalies of non-invertible symmetries for 2D QFTs from a string theory perspective. Our primary focus is on an infinite class of 2D QFTs engineered on D1-branes probing toric Calabi-Yau 4-fold singularities. We derive 3D SymTFTs from the topological sector of IIB supergravity and discuss the resulting 2D QFTs, which can be intrinsically relative or absolute. For intrinsically relative QFTs, we propose a sufficient condition for them to exist. For absolute QFTs, we show that they exhibit non-invertible symmetries with an elegant brane origin. Furthermore, we find that these non-invertible symmetries can suffer from anomalies, which we discuss from a top-down perspective. Explicit examples are provided, including theories for Y(p,k)(ℙ2), Y(2,0)(ℙ1 × ℙ1), and ℂ4/ℤ4 geometries.

Probing Krylov complexity in scalar field theory with general temperatures

Krylov complexity characterizes the operator growth in the quantum many-body systems or quantum field theories. The existing literatures have studied the Krylov complexity in the low temperature limit in the quantum field theories. In this paper, we extend and systematically study the Krylov complexity and Krylov entropy in a scalar field theory with general temperatures. To this end, we propose a new method to calculate the Wightman power spectrum which allows us to compute the Lanczos coefficients and subsequently to study the Krylov complexity (entropy) in general temperatures. We find that the Lanczos coefficients and Krylov complexity (entropy) in the high temperature limit will behave somewhat differently from those studies in the low temperature limit. We give an explanation of why the Krylov complexity does not oscillate in the high-temperature region. Moreover, we uncover the transition temperature that separates the oscillating and monotonic increasing behavior of Krylov complexity.

Gravitationally dominated instantons and instability of dS, AdS and Minkowski spaces

We study the decay of the false vacuum in the regime where the quantum field theory analysis is not valid, since gravitational effects become important. This happens when the height of the barrier separating the false and the true vacuum is large, and it has implications for the instability of de Sitter, Minkowski and anti-de Sitter vacua. We carry out the calculations for a scalar field with a potential coupled to gravity, and work within the thin-wall approximation, where the bubble wall is thin compared to the size of the bubble. We show that the false de Sitter vacuum is unstable, independently of the height of the potential and the relative depth of the true vacuum compared to the false vacuum. The false Minkowski and anti-de Sitter vacua can be stable despite the existence of a lower energy true vacuum. However, when the relative depth of the true and false vacua exceeds a critical value, which depends on the potential of the false vacuum and the height of the barrier, then the false Minkowski and anti-de Sitter vacua become unstable. We calculate the probability for the decay of the false de Sitter, Minkowski and anti-de Sitter vacua, as a function of the parameters characterizing the field potential.

CFTD from TQFTD+1 via Holographic Tensor Network, and Precision Discretization of CFT2

We show that the path integral of conformal field theories in D dimensions (CFTD) can be constructed by solving for eigenstates of a renormalization group (RG) operator following from the Turaev-Viro formulation of a topological field theory (topological quantum field theory) (TQFT) in D+1 dimensions (TQFTD+1), explicitly realizing the holographic sandwich relation between a symmetric theory and a TQFT. Generically, exact eigenstates corresponding to symmetric TQFTD follow from Frobenius algebra in TQFTD+1. For D=2, we construct eigenstates that produce 2D rational CFT path integrals exactly, which curiously connect a continuous-field theoretic path integral with the Turaev-Viro state sum. We also devise and illustrate numerical methods for D=2, 3 to search for CFTD as phase transition points between symmetric TQFTD. Finally, since the RG operator is in fact an exact analytic holographic tensor network, we compute “bulk-boundary” correlators and compare them with the AdS/CFT dictionary at D=2. Promisingly, they are numerically compatible given our accuracy, although further works will be needed to explore the precise connection to the AdS/CFT correspondence. Published by the American Physical Society 2024

Deformations and homotopy theory for Rota–Baxter family algebras

The concept of Rota–Baxter family algebra is a generalization of Rota–Baxter algebra. It appears naturally in the algebraic aspects of renormalizations in quantum field theory. Rota–Baxter family algebras are closely related to dendriform family algebras. In this paper, we first construct an [Formula: see text]-algebra whose Maurer–Cartan elements correspond to Rota–Baxter family algebra structures. Using this characterization, we define the cohomology of a given Rota–Baxter family algebra. As an application of our cohomology, we study formal and infinitesimal deformations of a given Rota–Baxter family algebra. Next, we define the notion of a homotopy Rota–Baxter family algebra structure on a given [Formula: see text]-algebra. We end this paper by considering the homotopy version of dendriform family algebras and their relations with homotopy Rota–Baxter family algebras.

Fate of stringy noninvertible symmetries

Noninvertible symmetries in quantum field theory (QFT) generalize the familiar product rule of groups to a more general fusion rule. In many cases, gauged versions of these symmetries can be regarded as dual descriptions of invertible gauge symmetries. One may ask: are there any other types of noninvertible gauge symmetries? In theories with gravity we find a new form of noninvertible gauge symmetry that emerges in the limit of fundamental, tensionless strings. These stringy noninvertible gauge symmetries appear in standard examples such as non-Abelian orbifolds. Moving away from the tensionless limit always breaks these symmetries. We also find that both the conventional form of noninvertible gauge symmetries and these stringy generalizations are realized in AdS/CFT. Although generically broken, approximate noninvertible symmetries have implications for swampland constraints: in certain cases they can be used to prove the existence of towers of states related to the distance conjecture, and can sometimes explain the existence of slightly subextremal states which fill in the gaps in the sublattice weak gravity conjecture. Published by the American Physical Society 2024