Gauge-invariant Way Research Articles

Bulk-induced D-brane deformations and the string coupling constant

We consider computing the on-shell disk action of open-closed string field theory as a gauge-invariant way of capturing the shift in D-brane tension that is induced by a deformation of the bulk CFT. We study the effect of bulk matter deformations (both marginal and relevant) on a wide range of boundary conditions in a number of CFTs up to subleading (two-loop) order in perturbation theory. In all analyzed examples, we find that the shift in the g-function of the matter boundary state is always accompanied by a boundary-independent shift in the string coupling constant, whose leading behaviour is universally proportional to the sphere two-point function of the deforming bulk operator.

Separation of pair and single top quark production in tWb-associated final state using a neural network

The paper presents a method for separating the contribution of pair and single top quark production in tWb-associated final state using a neural network. The proposed method makes possible to calculate such processes in a gauge-invariant way with fully taking into account interference contributions and dividing the phase space into single-resonant and double-resonant regions, which is necessary to increase the accuracy of the search for possible deviations from the predictions of the Standard Model in these processes. To train the neural network, the optimized set of observables is used to separate single-resonance and double-resonance contributions to the overall process. The use of this method allows us to avoid the disadvantages inherent in the schemes used in collider physics for calculating the processes of tWb-associated top quark production with the removal of Feynman diagrams, which leads to violation of gauge invariance, or the addition of a subtraction scheme, which leads to the appearance of negative weights for the part of simulated events. The proposed method can be used to increase the efficiency of searching for deviations from the predictions of the Standard Model in the interaction of the top quark with the W boson and b quark.

Spin and orbital angular momentum of coherent photons in a waveguide

Spin angular momentum of a photon corresponds to a polarisation degree of freedom of lights, and such that various polarisation properties are coming from macroscopic manifestation of quantum-mechanical properties of lights. An orbital degree of freedom of lights is also manipulated to form a vortex of lights with orbital angular momentum, which is also quantised. However, it is considered that spin and orbital angular momentum of a photon cannot be split from the total orbital angular momentum in a gauge-invariant way. Here, we revisit this issue for a coherent monochromatic ray from a laser source, propagating in a waveguide. We obtained the helical components of spin and orbital angular momentum by the correspondence with the classical Ponyting vector. By applying a standard quantum field theory using a coherent state, we obtained the gauge-independent expressions of spin and orbital angular momentum operators. During the derivations, it was essential to take a finite cross-sectional area into account, which leads the finite longitudinal component along the direction of the propagation, which allows the splitting. Therefore, the finite mode profile was responsible to justify the splitting, which was not possible as far as we were using plane-wave expansions in a standard theory of quantum-electrodynamics (QED). Our results suggest spin and orbital angular momentum are well-defined quantum-mechanical freedoms at least for coherent photons propagating in a waveguide and in a vacuum with a finite mode profile.

The general Two-Higgs Doublet Model in a gauge-invariant form

In the general Two-Higgs Doublet Model it has been shown that the Higgs potential can be expressed in terms of gauge-independent quantities that transform covariantly under unitary mixing of the doublets. In particular, stability, electroweak symmetry breaking, and CP symmetry can be understood in a concise way, avoiding unphysical gauge degrees of freedom. We complete this program and show how all the masses, the trilinear and quartic scalar interactions, the gauge-boson-Higgs interactions, as well as the Yukawa couplings in the general THDM can be expressed in a gauge-invariant way.

Entanglement in the Quantum Hall Matrix Model

Characterizing the entanglement of matrix degrees of freedom is essential for understanding the holographic emergence of spacetime. The Quantum Hall Matrix Model is a gauged U(N ) matrix quantum mechanics with two matrices whose ground state is known exactly and describes an emergent spatial disk with incompressible bulk dynamics. We define and compute an entanglement entropy in the ground state associated to a cut through the disk. There are two contributions. A collective field describing the eigenvalues of one of the matrices gives a gauge-invariant chiral boundary mode leading to an expected logarithmic entanglement entropy. Further, the cut through the bulk splits certain ‘off-diagonal’ matrix elements that must be duplicated and associated to both sides of the cut. Sewing these duplicated modes together in a gauge-invariant way leads to a bulk ‘area law’ contribution to the entanglement entropy. All of these entropies are regularized by finite N.

Mod-two APS index and domain-wall fermion

We show a mathematical relation between the mod-two Atiyah–Patodi–Singer (APS) index of a massless Dirac operator and massive domain-wall fermion determinant. The domain-wall fermion is given on a closed manifold, which is extended from the original manifold with boundary, where we instead give a fermion mass term changing its sign at the location of the original boundary. This new setup does not need the APS boundary condition, which is non-local. A mathematical proof of equivalence between the two different formulations is given by two different evaluations of the same index of a Dirac operator on a higher-dimensional manifold. The domain-wall fermion allows us to separate the edge and bulk mode contributions in a natural but not in a gauge invariant way, which offers a straightforward description of the global anomaly inflow.

A new perspective on the electroweak phase transition in the Standard Model Effective Field Theory

A first-order Electroweak Phase Transition (EWPT) could explain the observed baryon-antibaryon asymmetry and its dynamics could yield a detectable gravitational wave signature, while the underlying physics would be within the reach of colliders. The Standard Model, however, predicts a crossover transition. We therefore study the EWPT in the Standard Model Effective Field Theory (SMEFT) including dimension-six operators. A first-order EWPT has previously been shown to be possible in the SMEFT. Phenomenology studies have focused on scenarios with a tree-level barrier between minima, which requires a negative Higgs quartic coupling and a new physics scale low enough to raise questions about the validity of the EFT approach. In this work we stress that a first-order EWPT is also possible when the barrier between minima is generated radiatively, the quartic coupling is positive, the scale of new physics is higher, and there is good agreement with experimental bounds. Our calculation is done in a consistent, gauge-invariant way, and we carefully analyze the scaling of parameters necessary to generate a barrier in the potential. We perform a global fit in the relevant parameter space and explicitly find the points with a first-order transition that agree with experimental data. We also briefly discuss the prospects for probing the allowed parameter space using di-Higgs production in colliders.

Energy and angular momentum in D-dimensional Kerr-Ads black holes — New formulation

Recently, it was shown that the conserved charges of asymptotically anti-de Sitter spacetimes can be written in an explicitly gauge-invariant way in terms of the linearized Riemann tensor and the Killing vectors. Here, we employ this construction to compute the mass and angular momenta of the [Formula: see text]-dimensional Kerr-AdS black holes, which is one of the most remarkable Einstein metrics generalizing the four-dimensional rotating black hole.

BRST analysis and BFV quantization of the generalized quantum rigid rotor

We identify a strong similarity among several distinct originally second-class systems, including both mechanical and field theory models, which can be naturally described in a gauge-invariant way. The canonical structure of such related systems is encoded into a gauge-invariant generalization of the quantum rigid rotor. We perform the BRST symmetry analysis and the BFV functional quantization for the mentioned gauge-invariant version of the generalized quantum rigid rotor. We obtain different equivalent effective actions according to specific gauge-fixing choices, showing explicitly their BRST symmetries. We apply and exemplify the ideas discussed to two particular models, namely, motion along an elliptical path and the [Formula: see text] nonlinear sigma model, showing that our results reproduce and connect previously unrelated known gauge-invariant systems.

Background field method and generalized field redefinitions in effective field theories

We show that in a spontaneously broken effective gauge field theory, quantized in a general background \(R_\xi \)-gauge, also the background fields undergo a non-linear (albeit background-gauge invariant) field redefinition induced by radiative corrections. This redefinition proves to be crucial in order to renormalize the coupling constants of gauge-invariant operators in a gauge-independent way. The classical background-quantum splitting is also in general non-linearly deformed (in a non gauge-invariant way) by radiative corrections. Remarkably, such deformations vanish in the Landau gauge, to all orders in the loop expansion.

Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons

In this work, we present the inverted harmonic oscillator (IHO) Hamiltonian as a paradigm to understand the quantum mechanics of scattering and time-decay in a diverse set of physical systems. As one of the generators of area preserving transformations, the IHO Hamiltonian can be studied as a dilatation generator, squeeze generator, a Lorentz boost generator, or a scattering potential. In establishing these different forms, we demonstrate the physics of the IHO that underlies phenomena as disparate as the Hawking–Unruh effect and scattering in the lowest Landau level (LLL) in quantum Hall systems. We derive the emergence of the IHO Hamiltonian in the LLL in a gauge invariant way and show its exact parallels with the Rindler Hamiltonian that describes quantum mechanics near event horizons. This approach of studying distinct physical systems with symmetries described by isomorphic Lie algebras through the emergent IHO Hamiltonian enables us to reinterpret geometric response in the lowest Landau level in terms of relativistic effects such as Wigner rotation. Further, the analytic scattering matrix of the IHO points to the existence of quasinormal modes (QNMs) in the spectrum, which have quantized time-decay rates. We present a way to access these QNMs through wave packet scattering, thus proposing a novel effect in quantum Hall point contact geometries that parallels those found in black holes.

Tidal forces are gravitational waves

In this paper we show in a covariant and gauge invariant way that in general relativity, tidal forces are actually a hidden form of gravitational waves. This must be so because gravitational effects cannot occur faster than the speed of light. Any two body gravitating system, where the bodies are orbiting around each other, may generate negligible gravitational waves, but it is via these waves that non-negligible tidal forces (causing shape distortions) act on these bodies. Although the tidal forces are caused by the electric part of the Weyl tensor, we transparently show that some small time varying magnetic part of the Weyl tensor with non zero curl must be present in the system that mediates the tidal forces via gravitational wave type effects. The outcome is a new test of whether gravitational effects propagate at the speed of light.

Implications of dark sector mixing on leptophilic scalar dark matter

We propose a new viable outlook to the mixing between a singlet and a doublet leptonic dark sector fields. This choice relaxes the dark matter (DM) search constraints on the quintessential scalar singlet DM as well as presents new opportunities for its detection in the lab. The mixing produces an arbitrary mass difference between the two components of the extra doublet in a gauge-invariant way, without introducing any new scale of electroweak symmetry breaking in the theory. It also provides a useful handle to distinguish between the dark sector particles of different isospins, which is a challenging task other-wise. As the dark leptons coannihilate non-trivially, the mixing effectively enhances the viable parameter space for the relic density constraint. In low DM mass regime, our analysis shows that with a non-zero mixing, it is possible to relax the existing indirect search bounds on the upper limit of the DM-Standard Model coupling. From the analysis of the 3tau +{E}_T^{mathrm{miss}} and mathrm{ell}tau +{E}_T^{mathrm{miss}} channels for LHC at sqrt{s} = 13 TeV, we show that one ensures the presence of the mixing parameter between the dark sector particles of the theory by looking at the peak and tail positions of the kinematic distributions. Even with a tweak in the values of other free parameters within the viable parameter region, the distinct peak and tail positions of the kinematic distributions remains a constant feature of the model. While both the channels present us the opportunity to detect the mixing signature at the LHC/HL-LHC, the former gives better results in terms of a larger region of mixing parameter. From the fiducial cross section, the projected statistical significance for the integrated luminosity, mathcal{L} = 3 ab−1, are shown for a combined parameter region obeying all the existing constraints, where there is the best possibility to detect such a signature.

Chirality imbalance and chiral magnetic effect under a parallel electromagnetic field

We study the time evolution of the chirality imbalance $n_5$ and the chiral magnetic effect (CME) under the external parallel electromagnetic fields without assuming the artificial chiral asymmetric source. We adopt the time-dependent Sauter-type electric and constant magnetic field, and obtain analytical solutions of the Dirac equation for a massive fermion. We use the point-split regularization to calculate the vacuum contribution in the gauge invariant way. As a result, we find that $n_5$ and CME current increase substantially as the electric field increases, and stay finite after the electric field is switched off. The chirality imbalance and CME current are shown to consist of a dominant contribution, which is essentially proportional to relativistic velocity, and a small oscillating part. We find a simple analytical relation between $n_5$ and the fermion pair-production rate from the vacuum. We also discuss dynamical origin of the chirality imbalance in detail.

Effective entropy of quantum fields coupled with gravity

Entanglement entropy, or von Neumann entropy, quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this paper, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a replica calculation. The replicated theory is defined as a gravitational path integral with multiple copies of the original boundary conditions, with a co-dimension-2 brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. We apply the formula to two example systems, a closed two-dimensional universe and a four-dimensional maximally extended Schwarzchild black hole. We discuss the analog of the effective entropy in random tensor network models, which provides more concrete understanding of quantum information properties in general dynamical geometries. We show that, in absence of a large boundary like in AdS space case, it is essential to introduce ancilla that couples to the original system, in order for correctly characterizing quantum states and correlation functions in the random tensor network. Using the superdensity operator formalism, we study the system with ancilla and show how quantum information in the entanglement island can be reconstructed in a state-dependent and observer-dependent map. We study the closed universe (without spatial boundary) case and discuss how it is related to open universe.

The first law of black hole mechanics in the Einstein-Maxwell theory revisited

We re-derive the first law of black hole mechanics in the context of the Einstein-Maxwell theory in a gauge-invariant way introducing “momentum maps” associated to field strengths and the vectors that generate their symmetries. These objects play the role of generalized thermodynamical potentials in the first law and satisfy generalized zeroth laws, as first observed in the context of principal gauge bundles by Prabhu, but they can be generalized to more complex situations. We test our ideas on the d-dimensional Reissner-Nordström-Tangherlini black hole.

Notes on polytopes, amplitudes and boundary configurations for Grassmannian string integrals

We continue the study of positive geometries underlying the Grassmannian string integrals, which are a class of “stringy canonical forms”, or stringy integrals, over the positive Grassmannian mod torus action, G+(k, n)/T . The leading order of any such stringy integral is given by the canonical function of a polytope, which can be obtained using the Minkowski sum of the Newton polytopes for the regulators of the integral, or equivalently given by the so-called scattering-equation map. The canonical function of the polytopes for Grassmannian string integrals, or the volume of their dual polytopes, is also known as the generalized bi-adjoint ϕ3 amplitudes. We compute all the linear functions for the facets which cut out the polytope for all cases up to n = 9, with up to k=4 and their parity conjugate cases. The main novelty of our computation is that we present these facets in a manifestly gauge-invariant and cyclic way, and identify the boundary configurations of G+(k, n)/T corresponding to these facets, which have nice geometric interpretations in terms of n points in (k−1)-dimensional space. All the facets and configurations we discovered up to n = 9 directly generalize to all n, although new types are still needed for higher n.

Dynamical symmetry breaking in Yang–Mills geometrodynamics

We are going to analyze through a first order perturbative formulation the local loss of symmetry when a source of non-Abelian Yang-Mills and gravitational fields interacts with an external agent that perturbes the original geometry associated to the source. Then, as the symmetry in Abelian and non-Abelian field structures in four-dimensional Lorentzian spacetimes is displayed through the existence of local orthogonal planes of symmetry that we previously called blades one and two, the loss of symmetry will be manifested by the tilting of these planes under the influence of the external agent. It was found already that there is an algorithm to block diagonalize the Yang-Mills field strength isospace projections in a local gauge invariant way. Independently, it was also found an algorithm to diagonalize the Yang-Mills stress-energy tensor in a gauge invariant way. Using these results and perturbative analysis from a previous manuscript dealing with the Abelian case, we are going to demonstrate how to develop an algorithm for constructing local energy-momentum conserved currents inside both local orthogonal planes. As the interaction proceeds, the planes are going to tilt perturbatively, and in this strict sense the original local symmetries will be lost. But we will prove that the new blades at the same point will correspond after the tilting generated by perturbation, to new symmetries, with associated new local currents, both on each new local planes of symmetry. Old symmetries will be broken, new will arise. There will be a local symmetry evolution in the non-Abelian case as well.

Double Prompt J/ψ Hadroproduction in the Parton Reggeization Approach with High-Energy Resummation.

We study double prompt J/ψ hadroproduction within the nonrelativistic-QCD factorization formalism adopting the parton Reggeization approach to treat initial-state radiation in a gauge invariant and infrared-safe way. We present first predictions for the cross section distributions in the transverse momenta of the subleading J/ψ meson and the J/ψ pair. Already at leading order in α_{s}, these predictions as well as those for the total cross section and its distributions in the invariant mass m_{ψψ} and the rapidity separation |Y| of the J/ψ pair nicely agree with recent ATLAS and CMS Collaboration measurements, except for the large-m_{ψψ} and large-|Y| regions, where the predictions substantially undershoot the data. In the latter regions, Balitsky-Fadin-Kuraev-Lipatov resummation is shown to enhance the cross sections by up to a factor of 2 and so to improve the description of the data.

Angular decorrelations in γ + 2jets events at high energies in the parton Reggeization approach

We study associated production of prompt photon and two jets at high energies in the framework of the parton Reggeization approach (PRA), which is based on multi-Regge factorization of hard processes and Lipatov’s effective theory of Reggeized gluons and quarks. In this approach, initial-state off-shell effects and transverse momenta of initial partons are included in a gauge-invariant way. We compute azimuthal angle difference spectra in [Formula: see text] + 2[Formula: see text]jets events and compare results with data from D0 Collaboration at the Tevatron. It was found that agreement between predictions and data can be achieved only under assumption on strong violation in transverse momentum ordering during initial-state quantum chromodynamics (QCD) evolution which corresponds multi-Regge kinematical regime instead of DGLAP picture.