Unitary Gauge Research Articles

Magnetic quivers from brane webs with O7+-planes

We consider the Higgs branch of 5d fixed points engineered using brane webs with an O7+-plane. We use the brane construction to propose a set of rules to extract the corresponding magnetic quivers. Such magnetic quivers are generically framed non-simply-laced quivers containing unitary as well as special unitary gauge nodes. We compute the Coulomb branch Hilbert series of the proposed magnetic quivers. In some specific cases, an alternative magnetic quiver can be obtained either using an ordinary brane web or a brane web with an O5-plane. In these cases, we find a match at the level of the Hilbert series.

A differential relation between the energy and electric charge of a dyon

The differential relation between the energy and electric charge of a dyon is derived. The relation expresses the derivative of the energy with respect to the electric charge in terms of the boundary value for the temporal component of the dyon's electromagnetic potential. The use of the Hamiltonian formalism and transition to the unitary gauge make it possible to show that this derivative is proportional to the phase frequency of the electrically charged massive gauge fields forming the dyon's core. It follows from the differential relation that the energy and electric charge of the non-BPS dyon cannot be arbitrarily large. Finally, the dyon's properties are investigated numerically at different values of the model parameters.

Real-time lattice gauge theory actions: Unitarity, convergence, and path integral contour deformations

The Wilson action for Euclidean lattice gauge theory defines a positive-definite transfer matrix that corresponds to a unitary lattice gauge theory time-evolution operator if analytically continued to real time. Hoshina, Fujii, and Kikukawa (HFK) recently pointed out that applying the Wilson action discretization to continuum real-time gauge theory does not lead to this, or any other, unitary theory and proposed an alternate real-time lattice gauge theory action that does result in a unitary real-time transfer matrix. The character expansion defining the HFK action is divergent, and in this work we apply a path integral contour deformation to obtain a convergent representation for $U(1)$ HFK path integrals suitable for numerical Monte Carlo calculations. We also introduce a class of real-time lattice gauge theory actions based on analytic continuation of the Euclidean heat-kernel action. Similar divergent sums are involved in defining these actions, but for one action in this class this divergence takes a particularly simple form, allowing construction of a path integral contour deformation that provides absolutely convergent representations for $U(1)$ and $SU(N)$ real-time lattice gauge theory path integrals. We perform proof-of-principle Monte Carlo calculations of real-time $U(1)$ and $SU(3)$ lattice gauge theory and verify that exact results for unitary time evolution of static quark-antiquark pairs in ($1+1$)D are reproduced.

Three dimensional mirror symmetry beyond ADE quivers and Argyres-Douglas theories

Mirror symmetry, a three dimensional mathcal{N} = 4 IR duality, has been studied in detail for quiver gauge theories of the ADE-type (as well as their affine versions) with unitary gauge groups. The A-type quivers (also known as linear quivers) and the associated mirror dualities have a particularly simple realization in terms of a Type IIB system of D3-D5-NS5-branes. In this paper, we present a systematic field theory prescription for constructing 3d mirror pairs beyond the ADE quiver gauge theories, starting from a dual pair of A-type quivers with unitary gauge groups. The construction involves a certain generalization of the S and the T operations, which arise in the context of the SL(2, ℤ) action on a 3d CFT with a U(1) 0-form global symmetry. We implement this construction in terms of two supersymmetric observables — the round sphere partition function and the superconformal index on S2 × S1. We discuss explicit examples of various (non-ADE) infinite families of mirror pairs that can be obtained in this fashion. In addition, we use the above construction to conjecture explicit 3d mathcal{N} = 4 Lagrangians for 3d SCFTs, which arise in the deep IR limit of certain Argyres-Douglas theories compactified on a circle.

Factorised 3d mathcal{N} = 4 orthosymplectic quivers

We study the moduli space of 3d mathcal{N} = 4 quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise into decoupled sectors. Each decoupled sector is described by a single quiver gauge theory with only unitary gauge nodes. The orthosymplectic quivers serve as magnetic quivers for 5d mathcal{N} = 1 superconformal field theories which can be engineered in type IIB string theories both with and without an O5 plane. We use this point of view to postulate the dual pairs of unitary and orthosymplectic quivers by deriving them as magnetic quivers of the 5d theory. We use this correspondence to conjecture exact highest weight generating functions for the Coulomb branch Hilbert series of the orthosymplectic quivers, and provide tests of these results by directly computing the Hilbert series for the orthosymplectic quivers in a series expansion.

Effects of the modification of gravity on the production of primordial black holes

The enhancement of the spectrum of primordial comoving curvature perturbation R can induce the production of primordial black holes (PBH) which could account for part of present day dark matter. As an example of the effects of the modification of gravity on the production of PBHs, we investigate the effects on the spectrum of R produced by the modification of gravity in the case of G-inflation, deriving the relation between the unitary gauge curvature perturbation ζ and the comoving curvature perturbation R, and identifying a background dependent enhancement function E which can induce large differences between the two gauge invariant variables. We use this relation to derive an equation for R, showing for the presence of a momentum dependent effective sound speed (MESS), associated to the intrinsic entropy which can arise in modified gravity theories, in agreement with the model independent MESS approach to cosmological perturbations.When ζ is not constant in time it is different from R, for example on sub-horizon scales, or in models exhibiting an anomalous super-horizon growth of ζ, but since this growth cannot last indefinitely, eventually they will coincide. We derive the general condition for super-horizon growth of ζ, showing that slow-roll violation is not necessary. Since the abundance of PBHs depends on the statistics of the peaks of the comoving density contrast, which is related to the spectrum of R, it is important to take into account these effects on the PBHs abundance in modified gravity theories.

Quadratic degenerate higher-order scalar-tensor theories revisited

We present a novel and remarkably simple formulation of degenerate higher-order scalar-tensor (DHOST) theories whose Lagrangian is quadratic in second derivatives of some scalar field. Using disformal transformations of the metric, we identify a special "frame" (or metric) for which the Lagrangian of quadratic DHOST theories reduces to the usual Einstein-Hilbert term plus a few terms that depend on simple geometric quantities characterizing the uniform scalar field hypersurfaces. In particular, for quadratic DHOST theories in the physically interesting class Ia, the Lagrangian simply consists of the Einstein-Hilbert term plus a term proportional to the three-dimensional scalar curvature of the uniform scalar field hypersurfaces. The classification of all quadratic DHOST theories becomes particularly transparent in this geometric reformulation, which also applies to scalar-tensor theories that are degenerate only in the unitary gauge.

Black hole interior in unitary gauge construction

A quantum system with a black hole accommodates two widely different, though physically equivalent, descriptions. In one description, based on global spacetime of general relativity, the existence of the interior region is manifest, while understanding unitarity requires nonperturbative quantum gravity effects such as replica wormholes. The other description adopts a manifestly unitary, or holographic, description, in which the interior emerges effectively as a collective phenomenon of fundamental degrees of freedom. In this paper we study the latter approach, which we refer to as the unitary gauge construction. In this picture, the formation of a black hole is signaled by the emergence of a surface (stretched horizon) possessing special dynamical properties: quantum chaos, fast scrambling, and low energy universality. These properties allow for constructing interior operators, as we do explicitly, without relying on details of microscopic physics. A key role is played by certain coarse modes in the zone region (hard modes), which determine the degrees of freedom relevant for the emergence of the interior. We study how the interior operators can or cannot be extended in the space of microstates and analyze irreducible errors associated with such extension. This reveals an intrinsic ambiguity of semiclassical theory formulated with a finite number of degrees of freedom. We provide an explicit prescription of calculating interior correlators in the effective theory, which describes only a finite region of spacetime. We study the issue of state dependence of interior operators in detail and discuss a connection of the resulting picture with the quantum error correction interpretation of holography.

New aspects of Argyres-Douglas theories and their dimensional reduction

Argyres-Douglas (AD) theories constitute an infinite class of superconformal field theories in four dimensions with a number of interesting properties. We study several new aspects of AD theories engineered in A-type class mathcal{S} with one irregular puncture of Type I or Type II and also a regular puncture. These include conformal manifolds, structures of the Higgs branch, as well as the three dimensional gauge theories coming from the reduction on a circle. We find that the latter admits a description in terms of a linear quiver with unitary and special unitary gauge groups, along with a number of twisted hypermultiplets. The origin of these twisted hypermultiplets is explained from the four dimensional perspective. We also propose the three dimensional mirror theories for such linear quivers. These provide explicit descriptions of the magnetic quivers of all the AD theories in question in terms of quiver diagrams with unitary gauge groups, together with a collection of free hypermultiplets. A number of quiver gauge theories presented in this paper are new and have not been studied elsewhere in the literature.

Hamiltonian analysis of Mimetic gravity with higher derivatives

Two types of mimetic gravity models with higher derivatives of the mimetic field are analyzed in the Hamiltonian formalism. For the first type of mimetic gravity, the Ricci scalar only couples to the mimetic field and we demonstrate the number of degrees of freedom (DOFs) is three. Then in both Einstein frame and Jordan frame, we perform the Hamiltonian analysis for the extended mimetic gravity with higher derivatives directly coupled to the Ricci scalar. We show that different from previous studies working at the cosmological perturbation level, where only three propagating DOFs show up, this generalized mimetic model, in general, has four DOFs. To understand this discrepancy, we consider the unitary gauge and find out that the number of DOFs reduces to three. We conclude that the reason why this system looks peculiar is that the Dirac matrix of all secondary constraints becomes singular in the unitary gauge, resulting in extra secondary constraints and thus reducing the number of DOFs. Furthermore, we give a simple example of a dynamic system to illustrate how gauge choice can affect the number of secondary constraints as well as the DOFs when the rank of the Dirac matrix is gauge dependent.

МУЛЬТИВЕРСУМ: ФІЛОСОФСЬКА РЕФЛЕКСІЯ НАД ТЕОРЕТИЧНИМИ ІДЕЯМИ ТА ЕМПІРИЧНИМИ ДАНИМИ

The cosmological conception of the Multiverse was formulated based on unitary gauge theories in the Physics of high energy. Theoretically expected, the quantum fluctuations of the original scalar field in a vacuum state and different variants of local symmetries breaking in the process of Early Universe expansion were the reasons for the cosmological idea of many possible worlds or Multiverse. Together with the inflationary cosmological model, these ideas successfully solved the problems of Big Bang theory with an explanation of observable quasi-Euclidean geometry in our world and isotropy and homogeneity of space on a mega-scale. New observational data, especially discovery of accelerative widening of space, so as the problem of dark matter and dark energy put for cosmology the new questions. These questions need to be philosophically comprehended. Professor Sergiy Krymsky offered an interesting understanding of the notion of "matter" in the situation of many worlds in the 80s. He considered each of the possible worlds as "matter, kept in its specificity", which existed in its own space and time with its set of elements, physical laws and constants. However, his considering the original vacuum state of scalar field as non-being is not satisfied because its heterogeneity defines further places for becoming of Galaxies. In this article, the author considers the ideas about the ontological status of the original state of the Early Universe in modern cosmological Multiverse theories and discusses the possible antinomies in these transcendental ideas and their difference from Kantian ones. Experience of solution the Kant’s antinomy in history of physics was taken into account. It was the second antinomy of discreetness / continuality. The solution was haven get in a way proposed by Kant, namely with empirical research and their theoretical explanations. Cosmological application of High Energy Physics gets it to transcendental ideas area, namely to the problem of our world becoming one of the possible worlds, just as a particular variant of first Kant's antinomy. However, formulation of antinomy connected with consideration of the ontological status of original state for becoming of our world has other categorical expressions than Kantian one. The front position belongs here to categories of possibility and actuality, which Kant did not include in the area of transcendental ideas, thinking that the contingency, connecting with possibility, must be changed by inevitable necessity in cognitive progress. On the contrary, contingency has the main place in modern cosmological scenarios, depending on multiple possibilities. So categories of possibility and actuality in the foundations of scientific theories need special attention. Now it touches upon at least two moments: the virtual particles as abstract objects of relativistic quantum theories and to the problem of understanding the ontological status of category "matter" in foundations of many world cosmology in the context of relations to categories "possibility", "actuality" and "reality".

Radiative decays of charged leptons as constraints of unitarity polygons for active-sterile neutrino mixing and CP violation

We calculate the rates of radiative beta ^- rightarrow alpha ^- + gamma decays for (alpha , beta ) = (e, mu ), (e, tau ) and (mu , tau ) by taking the unitary gauge in the (3+n) active-sterile neutrino mixing scheme, and make it clear that constraints on the unitarity of the 3times 3 Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix U extracted from beta ^- rightarrow alpha ^- + gamma decays in the minimal unitarity violation scheme differ from those obtained in the canonical seesaw mechanism with n heavy Majorana neutrinos by a factor 5/3. In such a natural seesaw case we show that the rates of beta ^- rightarrow alpha ^- + gamma can be used to cleanly and strongly constrain the effective apex of a unitarity polygon, and compare its geometry with the geometry of its three sub-triangles formed by two vectors U^{}_{alpha i} U^*_{beta i} and U^{}_{alpha j} U^*_{beta j} (for i ne j) in the complex plane. We find that the areas of such sub-triangles can be described in terms of the Jarlskog-like invariants of CP violation {{mathcal {J}}}^{ij}_{alpha beta }, and their small differences signify slight unitarity violation of the PMNS matrix U.

A string theory realization of special unitary quivers in 3 dimensions

We propose a string theory realization of three-dimensional mathcal{N} = 4 quiver gauge theories with special unitary gauge groups. This is most easily understood in type IIA string theory with D4-branes wrapped on holomorphic curves in local K3’s, by invoking the Stückelberg mechanism. From the type IIB perspective, this is understood as simply compactifying the familiar Hanany-Witten (HW) constructions on a T3. The mirror symmetry duals are easily derived. We illustrate this with various examples of mirror pairs.

Anatomy of Higgs boson decays into γγ and γZ within the electroweak chiral Lagrangian in the Rξ gauges

In this work we study the Higgs boson decays into two photons and into one photon and one $Z$ gauge boson within the context of the non-linear Effective Field Theory called the Electroweak Chiral Lagrangian. We present a detailed computation of the corresponding amplitudes to one-loop level in the covariant $R_\xi$ gauges. We assume that the fermionic loop contributions are as in the Standard Model and focus here just in the computation of the bosonic loop contributions. Our renormalization program and the anatomy of the various contributions participating in the $R_\xi$ gauges are fully explored. With this present computation we demonstrate the gauge invariance of the EChL result, not only for the case of on-shell Higgs boson, but also for the most general and interesting case of off-shell Higgs boson. We finally analyse and conclude on the special relevance of the Goldstone boson loops, in good agreement with the expected chiral loops behaviour in Chiral Lagrangians. We perform a systematic comparison with the corresponding computation of the Standard Model in the $R_\xi$ gauges and with the previous EChL results in the unitary gauge. This work represents the first computation within the EChL of these Higgs observables to one-loop in the most general $R_\xi$ gauges and with a full renormalization program description, not yet fully explored in the previous literature and which is different to the most frequently used in the linear Effective Field Theory (SMEFT).

Ensemble from coarse graining: Reconstructing the interior of an evaporating black hole

In understanding the quantum physics of a black hole, nonperturbative aspects of gravity play important roles. In particular, huge gauge redundancies of a gravitational theory at the nonperturbative level, which are much larger than the standard diffeomorphism and relate even spaces with different topologies, allow us to take different descriptions of a system. While the physical conclusions are the same in any description, the same physics may manifest itself in vastly different forms in descriptions based on different gauge choices. In this paper, we explore the relation between two such descriptions, which we refer to as the global gauge and unitary gauge constructions. The former is based on the global spacetime of general relativity, in which understanding unitarity requires the inclusion of subtle nonperturbative effects of gravity. The latter is based on a distant view of the black hole, in which unitarity is manifest but the existence of interior spacetime is obscured. These two descriptions are complementary. In this paper, we initiate the study of learning aspects of one construction through the analysis of the other. We find that the existence of near empty interior spacetime manifest in the global gauge construction is related to the maximally chaotic, fast scrambling, and universal dynamics of the horizon in the unitary gauge construction. We use the complementarity of the gauge choices to understand the ensemble nature of the gravitational path integral in global spacetime in terms of coarse graining and thermality in a single unitary theory that does not involve any ensemble nature at the fundamental level. We also discuss how the interior degrees of freedom are related with those in the exterior in the two constructions. This relation emerges most naturally as entanglement wedge reconstruction and the effective theory of the interior in the respective constructions.

\U0001d4a9 = 2 dualities and Z-extremization in three dimensions

We use localization techniques to study duality in \U0001d4a9 = 2 supersymmetric gauge theories in three dimensions. Specifically, we consider a duality due to Aharony involving unitary and symplectic gauge groups, which is similar to Seiberg duality in four dimensions, as well as related dualities involving Chern-Simons terms. These theories have the possibility of non trivial anomalous dimensions for the chiral multiplets and were previously difficult to examine. We use a matrix model to compute the partition functions on both sides of the duality, deformed by real mass and FI terms. The results provide strong evidence for the validity of the proposed dualities. We also comment on a recent proposal for recovering the exact IR conformal dimensions in such theories using localization.

The role of U(1)\u2019s in 5d theories, Higgs branches, and geometry

We explore the Higgs branches of five-dimensional mathcal{N} = 1 quiver gauge theories at finite coupling from the paradigm of M-theory on local Calabi-Yau threefolds described as ℂ∗-fibrations over local K3’s. By properly counting local deformations of singularities, we find results compatible with unitary as opposed to special unitary gauge groups. We interpret these results by dualizing to both IIA on local K3’s with D6-branes, and to IIB with 5-branes. Finally, we find that, by compactifying the ℂ∗-fibers to tori, a well-known Stückelberg mechanism eliminates Abelian factors, and provides missing Higgs branch moduli in a very interesting way. This is also explained from the dual IIA and IIB viewpoints.

Renormalization in an interpolating gauge in Yang–Mills theory

The Coulomb gauge in QCD is the only explicitly unitary gauge. But it suffers from energy-divergences which means that it is not rigorously well-defined. One way to define it unambiguously is as the limit of a gauge interpolating between the Feynman gauge and the Coulomb gauge. This interpolating gauge is characterized by a parameter θ and the Coulomb gauge is obtained in the limit θ→0. We study the renormalization of this θ-gauge for all values of θ. Novel features include field mixing as well as scaling, the renormalization of the θ parameter itself, and the appearance of new counter-term structures at two-loop order.

Electroweak fermion triangle loop contributions to the muon anomalous magnetic moment revisited

Abstract The contribution to the muon anomalous magnetic moment from the fermion triangle loop diagrams connected to the muon line by a photon and a $Z$ boson is re-analyzed in both the unitary gauge and the ’t Hooft–Feynman gauge. With use of the anomalous axial-vector Ward identity, it is shown that the calculation in the unitary gauge exactly coincides with the one in the ’t Hooft–Feynman gauge. The part which arises from the ordinary axial-vector Ward identity corresponds to the contribution of the neutral Goldstone boson. For the top-quark contribution, the one-parameter integral form is obtained up to the order of $m_\mu^2/m_Z^2$. The results are compared with those obtained by the asymptotic expansion method.

Abelian Higgs model in power-law inflation: the propagators in the unitary gauge

We consider the Abelian Higgs model in the broken phase as a spectator in cosmological spaces of general D space-time dimensions, and allow for the condensate to be time-dependent. We fix the unitary gauge using Dirac’s formalism for constrained systems, and then quantize the gauge-fixed system. Vector and scalar perturbations develop time­dependent masses. We work out their propagators assuming the cosmological background is that of power-law inflation, characterized by a constant principal slow-roll parameter, and that the scalar condensate is in the attractor regime, scaling as the Hubble rate. Our propagators correctly reduce to known results in the Minkowski and de Sitter space limits. We use the vector propagator to compute the equal-time correlators of electric and magnetic fields and find that at super-Rubble separations the former is enhanced, while the latter is suppressed compared to the vacuum fluctuations of the massless vector field. These correlators satisfy the hierarchy governed by Faraday’s law.