Narrow Results

In this paper we revisit the subject of anomaly cancelation in string theory and M-theory on manifolds with string structure and give three observations. First, that on string manifolds there is no E₈ × E₈ global anomaly in heterotic string theory. Second, that the description of the anomaly in the phase of the M-theory partition function of Diaconescu–Moore–Witten extends from the spin case to the string case. Third, that the cubic refinement law of Diaconescu–Freed–Moore for the phase of the M-theory partition function extends to string manifolds. The analysis relies on extending from invariants which depend on the spin structure to invariants which instead depend on the string structure. Along the way, the one-loop term is refined via the Witten genus.

Experimental era of rare $B$-decays started with the measurement of $B\to K^{\ast }\gamma$ by CLEO in 1993, followed by the measurement of the inclusive decay $B\to X_s\gamma$ in 1995, which serves as the standard candle in this field. The frontier has moved in the meanwhile to the experiments at the LHC, in particular, LHCb, with the decay $B^0\to {\mu }^{+}{\mu }^{-}$ at about 1 part in 10${}^{10}$ being the smallest branching fraction measured so far. Experimental precision achieved in this area has put the standard model to unprecedented stringent tests and more are in the offing in the near future. I review some key measurements in radiative, semileptonic and leptonic rare $B$-decays, contrast them with their estimates in the SM, and focus on several mismatches reported recently. They are too numerous to be ignored, yet, standing alone, none of them is significant enough to warrant the breakdown of the SM. Rare $B$-decays find themselves at the crossroads, possibly pointing to new horizons, but quite likely requiring an improved theoretical description in the context of the SM. An independent precision experiment such as Belle II may help greatly in clearing some of the current experimental issues.

In this paper, we discuss the chiral anomaly in a Lorentz-breaking extension of QED which, besides the common terms that are present in the Standard Model Extension, includes some dimension-five nonminimal couplings. We find, using the Fujikawa formalism, that these nonminimal couplings induce new terms in the anomaly which depend on the Lorentz-violating parameters. Perturbative calculations are also carried out in order to investigate whether new ambiguous Carroll–Field–Jackiw terms are induced in the effective action.

The two-dimensional minimal supersymmetric sigma models with homogeneous target spaces $G/H$ and chiral fermions of the same chirality are revisited. In particular, we look into the isometry anomalies in $\mathrm{\text{O}}(N)$ and $\mathrm{\text{CP}}(N-1)$ models. These anomalies are generated by fermion loop diagrams which we explicitly calculate. In the case of $\mathrm{\text{O}}(N)$ sigma models the first Pontryagin class vanishes, so there is no global obstruction for the minimal ${𝒩}=(0,1)$ supersymmetrization of these models. We show that at the local level isometries in these models can be made anomaly free by specifying the counterterms explicitly. Thus, there are no obstructions to quantizing the minimal ${𝒩}=(0,1)$ models with the $S^{N-1}=\mathrm{\text{SO}}(N)/\mathrm{\text{SO}}(N-1)$ target space while preserving the isometries. This also includes $\mathrm{\text{CP}}(1)$ (equivalent to $S^2$) which is an exceptional case from the $\mathrm{\text{CP}}(N-1)$ series. For other $\mathrm{\text{CP}}(N-1)$ models, the isometry anomalies cannot be rescued even locally, this leads us to a discussion on the relation between the geometric and gauged formulations of the $\mathrm{\text{CP}}(N-1)$ models to compare the original of different anomalies. A dual formalism of $\mathrm{\text{O}}(N)$ model is also given, in order to show the consistency of our isometry anomaly analysis in different formalisms. The concrete counterterms to be added, however, will be formalism dependent.

An explicit and detailed investigation about the two-dimensional (2D) single and triple axial-vector triangles is presented. Such amplitudes are related to the 2D axial-vector two-point function (AV) through contractions with the external momenta. Given this fact, before considering the triangles, we give a clear point of view for the AV anomalous amplitude. Such point of view is constructed within the context of an alternative strategy to handle the divergences typical of the perturbative solutions of quantum field theory. In the referred procedure all amplitudes in all theories, formulated in odd and even space–time dimensions, renormalizable or not, are treated on the same footing. After performing, in a very detailed way, all the calculations, we conclude that the same phenomenon occurring in the AV amplitude is present also in the finite single and triple axial-vector triangles. The conclusion gives support to the thesis that the phenomenon is present in pseudo-amplitudes belonging to a chain where the divergent AV one is only the simplest structure. It is expected that the same must occur in all even space–time dimensions. In particular, in four dimensions, the single and triple axial box amplitudes must exhibit anomalies too.

In earlier work we analyzed an abelianized model in which a gauged Rarita–Schwinger spin-$\frac{3}{2}$ field is directly coupled to a spin-$\frac{1}{2}$ field. Here, we extend this analysis to the gauged $SU(8)$ model for which the abelianized model was a simplified substitute. We calculate the gauge anomaly, show that anomaly cancellation requires adding an additional left chiral representation $\bar{8}$ spin-$\frac{1}{2}$ fermion to the original fermion complement of the $SU(8)$ model, and give options for restoring boson–fermion balance. We conclude with a summary of attractive features of the reformulated $SU(8)$ model, including a possible connection to the $E_8$ root lattice.

We study the new extension of the $z=3$ Horava–Lifshitz QED involving a CPT-breaking term, characterized by the axial vector $b_{0,i}$, and calculate the Carroll–Field–Jackiw (CFJ) term in the one-loop approximation. Explicitly, we use two regularization schemes and demonstrate that in our case, the CFJ term is finite but ambiguous, so that its exact coefficient depends on the used regularization.

A grand unification scenario is presented that is based on quantum field theory, and where a single $E_8$ gauge superfield in 10 dimensions is used to obtain all the particle content of the Standard Model at low energies. The key feature of the formulation lies in the dimensional reduction used to break the gauge symmetry and to determine the low energy spectrum. It is shown that, through the orbifold $T^6/({\mathbb{Z}}_6\times {\mathbb{Z}}_2)$, and its corresponding Wilson lines, the symmetry is broken to the Standard Model one, generating a particular model that includes the Minimal Supersymmetric Standard Model spectrum. Furthermore it is also shown that the model is free of gauge anomalies at all levels by itself, i.e. without the need to include any additional representations of fields. Thus a complete unification of the Standard Model into a single gauge superfield is shown to be formally plausible. Although this paper does not include a phenomenological study of the specific model (currently being investigated), some interesting questions and observations are included as motivation for the scenario.

In this paper, we apply decomposition to orbifolds with quantum symmetries to resolve anomalies. Briefly, it has been argued by, e.g. Wang–Wen–Witten, Tachikawa that an anomalous orbifold can sometimes be resolved by enlarging the orbifold group so that the pullback of the anomaly to the larger orbifold group is trivial. For this procedure to resolve the anomaly, one must specify a set of phases in the larger orbifold, whose form is implicit in the extension construction. There are multiple choices of consistent phases, which give rise to physically distinct resolutions. We apply decomposition, and find that theories with enlarged orbifold groups are equivalent to (disjoint unions of copies of) orbifolds by nonanomalous subgroups of the original orbifold group. In effect, decomposition implies that enlarging the orbifold group is equivalent to making it smaller. We provide a general conjecture for such descriptions, which we check in a number of examples.

After many years of investigations, our understanding of the dynamics of strongly coupled chiral gauge theories is still quite unsatisfactory today. Conventional wisdom about strongly coupled gauge theories, successfully applied to QCD, is not always as useful in chiral gauge theories. Recently, some new ideas and techniques have been developed, which involve concepts of generalized symmetries, of gauging a discrete center symmetry, and of generalizing the ’t Hooft anomaly matching constraints to include certain mixed symmetries. This new development has been applied to chiral gauge theories, leading to many interesting, sometimes quite unexpected, results. For instance, in the context of generalized Bars–Yankielowicz and generalized Georgi–Glashow models, these new types of anomalies give a rather clear indication in favor of the dynamical Higgs phase, against confining, flavor symmetric vacua.

Another closely related topic is strong anomaly and the effective low-energy action representing it. It turns out that they have significant implications on the phase of chiral gauge theories, giving indications consistent with the findings based on the generalized anomalies.

Some striking analogies and contrasts between the massless QCD and chiral gauge theories seem to emerge from these discussions. The aim of this work is to review these developments.

We study massive scalar fields and Dirac fields propagating in a five-dimensional dilatonic black hole background. We expose that for both fields the physics can be described by a two-dimensional theory, near the horizon. Then, in this limit, by applying the covariant anomalies method we find the Hawking flux by restoring the gauge invariance and the general coordinate covariance, which coincides with the flux obtained from integrating the Planck distribution for fermions.

Vacuum fluctuations of quantum fields are altered in the presence of a strong gravitational background, with important physical consequences. We argue that a nontrivial spacetime geometry can act as an optically active medium for quantum electromagnetic radiation, in such a way that the state of polarization of radiation changes in time, even in the absence of electromagnetic sources. This is a quantum effect, and is a consequence of an anomaly related to the classical invariance under electric-magnetic duality rotations in Maxwell theory.

In the presence of rotation, gravity induces, even at zero temperature, a chiral vortical current. This current is interpreted as emerging from the gravitational Chern–Simons current. We argue that this gravitational Chern–Simons chiral vortical current may provide a novel universal microscopic mechanism behind the generation of collimated jets from rotating astrophysical compact sources.

A procedure confirms whether a return-factor correlation is anomalous or results from endogenous simultaneous-equations bias. The identification strategy sorts the cost of capital components for instruments. In the first stage, the initially found factors are regressed on cost instruments. In the second stage, a confirmed anomaly has predicted value significant in returns and exogenous.

Taxes, depreciation and capital structure are strong instruments, affecting 1980–2017 quarterly U.S. stock returns. Size, value and profitability decisions are significant in instruments. Returns increase in fitted profits, but not small size. Actual and predicted values have weaker correlation with returns over time.

Cloud computing forms a mainstream in the emerging field of Internet of Things (IoT) networks, which provides high storage and access to data whenever needed. The cloud architecture is highly vulnerable to various anomalies due to the centralised process that has the capability of ruining the reputation or causing the loss of trust in an organisation. Preventing anomalies in cloud architecture extends the lifetime of the system and increases privacy preservation. In this research, blockchain technology is adopted for facilitating secure communication in the network, and anomaly detection is performed using the proposed Hexabullus optimisation-based Fuzzy classifier based on the entropy-based rules. The importance of this research relies on the calculation of entropy and anomaly detection using optimal rules generated using the proposed hexabullus optimisation. The experimental results show that the proposed blockchain-enabled cloud architecture prevents the occurrence of attacks more efficiently. The proposed hexabullus optimisation-based anomaly detection is evaluated with existing methods that attained an improved accuracy of 88%, precision of 88%, and recall of 90%, which is highly efficient in rendering the secure communication of the data in the cloud.

Most of the known models describing the fundamental interactions have a gauge freedom. In the standard path integral, it is necessary to "fix the gauge" in order to avoid integrating over unphysical degrees of freedom. Gauge independence might then become a tricky issue, especially when the structure of the gauge symmetries is intricate. In the modern approach to this question, it is the BRST invariance that effectively implements the gauge invariance. This set of lectures briefly reviews some key ideas underlying the BRST-antifield formalism, which yields a systematic procedure to path-integrate any type of gauge system, while (usually) manifestly preserving space–time covariance. The quantized theory possesses a global invariance under the so-called BRST transformation, which is nilpotent of order two. The cohomology of the BRST differential is the central element that controls the physics. Its relationship with the observables is sketched and explained. How anomalies appear in the "quantum master equation" of the antifield formalism is also discussed. These notes are based on the lectures given by MH at the 10th Saalburg Summer School on Modern Theoretical Methods from the 30th of August to the 10th of September, 2004 in Wolfersdorf, Germany and were prepared by AF and AM. The exercises which were discussed at the school are also included.

Studying the M-branes leads us naturally to new structures that we call Membrane-, Membrane^c, String^K(ℤ,3) and Fivebrane^K(ℤ,4) structures, which we show can also have twisted counterparts. We study some of their basic properties, highlight analogies with structures associated with lower levels of the Whitehead tower of the orthogonal group, and demonstrate the relations to M-branes.

Studying the topological aspects of M-branes in M-theory leads to various structures related to Wu classes. First we interpret Wu classes themselves as twisted classes and then define twisted notions of Wu structures. These generalize many known structures, including Pin^- structures, twisted Spin structures in the sense of Distler–Freed–Moore, Wu-twisted differential cocycles appearing in the work of Belov–Moore, as well as ones introduced by the author, such as twisted Membrane and twisted String^c structures. In addition, we introduce Wu^c structures, which generalize Pin^c structures, as well as their twisted versions. We show how these structures generalize and encode the usual structures defined via Stiefel–Whitney classes.

We perform a class of nonlinear extensions of the reparametrization algebra at arbitrary dimensions. Our extended algebras reproduce in the one-dimensional limit the well-known -ones. We point out the existence of a family of reparametrization invariant functions for which this property is untouched by the extension procedure. This allows to calculate the improvement of the gravitational anomaly within the extended symmetry.

We consider gauge models in the causal approach and study one-loop contributions to the chronological products and the anomalies they produce. We prove that in order greater than 4 there are no one-loop anomalies. Next we analyze one-loop anomalies in the second- and third-order of the perturbation theory. We prove that the even parity contributions (with respect to parity) do not produce anomalies; for the odd parity contributions we reobtain the well-known result.