Gauge anomaly cancellation in chiral gauge theories

We consider chiral fermions interacting minimally with abelian and non-abelian gauge fields. Using a path integral approach and exploring the consequences of a mechanism of symmetry restoration, we show that the gauge anomaly has null expectation value in the vacuum for both cases (abelian and non-abelian). We argue that the same mechanism has no possibility to cancel the chiral anomaly, what eliminates competition between chiral and gauge symmetry at full quantum level. We also show that the insertion of the gauge anomaly in arbitrary gauge invariant correlators gives a null result, which points towards anomaly cancellation in the subspace of physical state vectors.     

Parity anomalies in gauge theories in 2 + 1 dimensions

It is shown that the introduction of massless fermions in an abelian gauge theory in 2 + 1 dimensions does not lead to any parity anomaly despite a non-commutativity of limits in the structure function of the odd part of the vacuum polarisation tensor. However, a parity anomaly does exist in non-abelian theories due to a conflict between gauge invariance under large gauge transformations and the parity symmetry.     

An explicit example of a tumbling gauge theory

We present a class of two-dimensional models with a non-abelian gauge symmetry. In one model with gauge symmetry is dynamically broken by a fermion bilinear condensate in a $\text{1}\text{n}$ expansion. We discuss the differences between a dynamical and elementary Higgs mechanism due to the presence of a non-abelian axial anomaly.     

A theorem on electromagnetic properties of leptons

The following theorem is proven: Every lepton with the mass m, electric charge q and spin J belonging to any representation of a non-abelian gauge group must have the magnetic moment μ = qJm^?1, electric mean squared radius r² = qJ(J + 1)m^?2 and electric quadrupole moment Q = qJ(2J ? 1)m^?2 in the first order of the electromagnetic effects in an arbitrary renormalizable theory with the non-abelian gauge group symmetry which permits the validity of the Gerasimow-Drell-Hearn and Cabibbo-Radicati sum rules. The formula for the magnetic moment applies also for an abelian symmetry and remains valid even if the gauge symmetry is spontaneously broken.     

Gravitational Contributions to the Running of Gauge Couplings

Gravitational contributions to the running of gauge couplings arecalculated by using different regularization schemes. As the β function concerns counter-terms of dimension four, only quadratic divergences from the gravitational contributions need to be investigated. A consistent result is obtained by using a symmetry-preserving loop regularization with string-mode regulators which can appropriately treat the quadratic divergences andpreserve non-abelian gauge symmetry. The harmonic gauge conditionfor gravity is used in both diagrammatical and background field calculations, the resulting gravitational corrections to the β function are found to be nonzero, which is different from previous results presented in the existing literatures.     

Heavy-particle-induced effective lagrangian in spontaneously broken theories (II). The abelian Higgs-Kibble model

In the context of the abelian Higgs-Kibble model with a charged fermion, we study in detail low-energy effective field theories of light particles when the heavy mass scales in the theory are generated by the Higgs-Kibble mechanism. Our analysis is based on the systematic use of factorization methods, and is valid to all orders in renormalized perturbation theory. Emphasis is given to finding the vestiges of the original (spontaneously broken) local gauge symmetry left in low-energy effective field theories, and general techniques are developed for that purpose. When only Fermi fields or / and physical Higgs fields correspond to light particles, low-energy effective field theories do not exhibit such signs. On the other hand, when physical gauge fields (together with other unphysical fields) correspond to light particles, the original local gauge symmetry restricts the resulting low-energy effective local action to a non-trivial form.     

Origins of global anomalies in quantum mechanics

Simple and tractable examples of abelian and non-abelian gauge systems with global anomalies are presented in quantum mechanics. Explicit calculations are done both in the path-integral and hamiltonian formalism. Algebraic criteria are given for the existence of global gauge anomalies. These criteria are applied for every gauge group and many representations. The inconsistency of theories with a global gauge anomaly is discussed.     

各级微扰展开下自发破缺的规范无关性、么正性及可重整性

用微扰论展开明显地讨论了标粒子与规范场矢粒子自发破缺Abel模型,发现在各种可重整规范下同阶各费曼图的内线非物理分量贡献的规范有关部分只与外线的质壳外部分互相依存。在质壳上只剩下物理分量的贡献,亦即转化成了么正规范。这样就明显地验证了么正规范与可重整规范在质壳上的全同,从而说明可重整规范是么正的,以及么正规范下怎样会出现剩余发散,为何剩余发散必然相消,揭穿了么正规范的隐藏可重整性。     

A Pati–Salam model from branes

We explore the possibility of embedding the Pati–Salam model in the context of Type I brane models. We study a generic model with U(4)_C×U(2)_L×U(2)_R gauge symmetry and matter fields compatible with a Type I brane configuration. Examining the anomaly cancellation conditions of the surplus abelian symmetries we find an alternative hypercharge embedding that is compatible with a low string/brane scale of the order of 5–7 TeV, when the U(4)_C and U(2)_R brane stack couplings are equal. Proton stability is assured as baryon number is associated to a global symmetry remnant of the broken abelian factors. It is also shown that this scenario can accommodate an extra low energy abelian symmetry that can be associated to lepton number. The issue of fermion and especially neutrino masses is also discussed.     

Spontaneously broken supergauge symmetries and goldstone spinors

We present a model with a spontaneously broken supergauge symmetry which results in the appearance of a massless Goldstone spinor. The model combines supergauge invariance with ordinary gauge invariance. After the breaking the gauge boson acquires a mass as a result of the Higgs mechanism.     

Electroweak Sudakov logarithms and real gauge-boson radiation in the TeV region

Electroweak radiative corrections give rise to large negative, double-logarithmically enhanced corrections in the TeV region. These are partly compensated by real radiation and, moreover, affected by selecting isospin-non-invariant external states. We investigate the impact of real gauge boson radiation more quantitatively by considering different restricted final state configurations. We consider successively a massive abelian gauge theory, a spontaneously broken SU(2) theory and the electroweak Standard Model. We find that details of the choice of the phase space cuts, in particular whether a fraction of collinear and soft radiation is included, have a strong impact on the relative amount of real and virtual corrections.     

Spontaneous symmetry breaking in the non-abelian anyon fluid

We study the theory of non-relativistic matter coupled to the non-Abelian U(2) Chem-Simons gauge field in (2 + 1) dimensions. We adopt the mean-field approximation in the current algebra formulation already applied to the abelian anyons. We first show that this method is able to describe both “boson-based” and “fermion-based” anyons and yields consistent results over the whole range of fractional statistics. In the non-abelian theory, we find a superfluid (and superconductive) phase, which is smoothly connected with the abelian superfluid phase originally discovered by Laughlin. The characteristic massless excitation is the Goldstone particle of the specific mechanism of spontaneous symmetry breaking. An additional massive mode is found by diagonalizing the non-local, non-abelian hamiltonian in the radial gauge.     

On the random vector potential model in two dimensions

The random vector potential model describes massless fermions coupled to a quenched random gauge field. We study its abelian and non-abelian versions. The abelian version can be completely solved using bosonization. We analyse the non-abelian model using its supersymmetric formulation and show, by a perturbative renormalization group computation, that it is asymptotically free at large distances. We also show that all the quenched chiral current correlation functions can be computed exactly, without using the replica trick or the supersymmetric formulation, but using an exact expression for the effective action for any sample of the random gauge field. These chiral correlation functions are purely algebraic.     

Nonlocal regularization and spontaneously broken abelian gauge theories for an arbitrary gauge parameter

We study the nonlocal regularization for the case of a spontaneously broken abelian gauge theory in the R-gauge with an arbitrary gauge parameter . We consider a simple abelian-Higgs model with chiral couplings as an example. We show that if we apply the nonlocal regularization procedure (to construct a nonlocal theory with FINITE mass parameter) to the spontaneously broken R-gauge Lagrangian, using the quadratic forms as appearing in this Lagrangian, we find that a physical observable in this model, an analogue of the muon anomalous magnetic moment, evaluated to order O [g²] does indeed show -dependence. We then apply the modified form of nonlocal regularization that was recently advanced and studied for the unbroken non-abelian gauge theories and discuss the resulting WT identities and -independence of the S-matrix elements.     

Interacting fermions on a random lattice

We extend previous work on the properties of the Dirac lagrangian on two-dimensional random lattices to the case where interaction terms are included. Although for free fermions the chiral symmetry of the doubles is spontaneously broken by their interaction with the lattice and they decouple from long-distance physics, our results in this paper show that all is undone by quantum corrections in an interacting field theory and that the end result is very similar to what is found with Wilson fermions. Two field-theoretical models with interacting fermions are studied by perturbation expansion in the field theory coupling constant. These are a model with one fermion and one boson species interacting via a scalar Yukawa coupling and the massive Thirring model. It is shown that on the random lattice ultraviolet finite diagrams and finite parts of ultraviolet divergent diagrams have the correct continuum limit. Ultraviolet divergent parts can be removed by the same renormalisation procedure as in the continuum, but do not exhibit the same dependence on the lagrangian mass. In the case of the massive Thirring model this causes a fermion mass correction of order the cut-off scale, which breaks the chiral symmetry of the remaining light fermion; there is consequently a fine-tuning problem. In the context of the same model we discuss the effect of the Goldstone boson associated with the spontaneous breakdown of the chiral symmetry of the doubles on two-dimensional models with vector couplings.     

S-duality of color-ordered amplitudes

Recently, it has been proposed that the S-matrix elements on the world volume of an abelian D₃-brane are consistent with the Ward identity associated with the S-duality. In this paper we extend this study to the case of multiple D₃-branes. We speculate that the S-matrix elements are consistent with the S-dual Ward identity irrespective of the ordering of the external states. Imposing this symmetry on the particular case of the S-matrix element of one Kalb–Ramond, one transverse scalar and two non-abelian gauge bosons, we will find the linear S-duality transformation of the commutator of two non-abelian gauge field strengths. Using this transformation and the standard S-duality transformations of the supergravity fields, all other non-abelian S-matrix elements of one closed and three open string states can be found by the S-duality proposal. We will show that the predicted S-matrix elements are reproduced exactly by explicit calculations.     

On the induced cosmological term in quantum gravity

Tadpole diagrams where zero-momentum gravitons couple to massive matter loops lead to divergences which are not a consequence of infinite momentum integrals, but of the masslessness of the gravitons. It is shown that there exists no definition of these diagrams consistent with the Ward identities. They can be eliminated by an appropriate gauge choice, but then the BRS symmetry is spontaneously broken. Also in the scalar-tensor, conformally invariant formulation of quantum gravity, the tadpole problem does survive. The tadpole diagrams can, however, be cancelled by a cosmological counter-term. In that case, the Ward identities are satisfied.     

Standard Model Gauge Couplings from Gauge-Dilatation Symmetry Breaking

It is well known that the self-energy of the gauge bosons is quadratically divergent in the Standard Model when a simple cutoff is imposed. We demonstrate phenomenologically that the quadratic divergences in fact unify. The unification occurs at a surprisingly low scale, \(\Lambda _\mathrm {u}\approx 4\times 10^7\)  GeV. Suppose now that there is a spontaneously broken rotational symmetry between the space-time coordinates and gauge theoretical phases. The symmetry-breaking pattern is such that the gauge bosons arise as the massless Goldstone bosons, whereas the dilatonic mode acts as the massive (Higgs) boson, whose vacuum expectation value determines the gauge couplings. In this case, the quadratic divergences or the tadpoles of the gauge boson self-energy should indeed unify because these divergences need to be cancelled by a universal dilatonic contribution, assuming dynamical symmetry breaking. If there is dynamical symmetry breaking, we are in principle able to calculate the value of the gauge couplings as well as the scale hierarchy \(\Lambda _\mathrm {cut}/\Lambda _\mathrm {u}\) . We perform this calculation by adopting a naive quartic symmetry-breaking potential which unfortunately violates local gauge invariance. Using tadpole-cancellation and dilatonic self-energy conditions, the value of \(\Lambda _\mathrm {cut}\) is then found to be approximately \(4\times 10^{18}\)  GeV in the Feynman gauge and \(5\times 10^{15}\)  GeV in the Landau gauge. The cancellation of an anomaly in the dilaton self-energy requires that the number of fermionic generations equals three. The symmetry-breaking needs to be driven by some other mass-generating mechanism such as electroweak symmetry breaking. Our estimation for \(\Lambda _\mathrm {u}\) is of the correct order if \(\Lambda _\mathrm {cut}\approx 5\times 10^{15}\)  GeV.     

Pseudo-Goldstone boson masses in a one-loop approximation

A one-loop calculation of pseudo-Goldstone boson masses in a spontaneously broken gauge model indicates that they are either identically zero or too large (of the order of several GeV) to be identified with the pion masses. The former possibility, which suggests that the pion mass may have its origin in even higher order weak and electromagnetic corrections, is investigated.     

Spontaneous symmetry breakdown in the abelian Higgs model

For the abelian Higgs model we introduce a new gauge invariant observable which in Landau gauge is . In three or more dimensions this observable is used to show that the global gauge symmetry is spontaneously broken in the lattice theory for a suitable range of parameters. This observable also provides a gauge invariant order parameter for the phase transition in this model.Research supported by U.S. National Science Foundation grant PHY8116101-A03Research supported by U.S. National Science Foundation grant PHY8117463