International Journal of Modern Physics A

I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of nonlinear realisations and Kac–Moody algebras, I explain how to construct the nonlinear realisation based on the Kac–Moody algebra $E_{11}$ and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a space–time with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of space–time, lead to precisely the equations of motion of 11-dimensional supergravity theory. By taking different group decompositions of $E_{11}$ we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the nonlinear realisation should be thought of as a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the $E_{11}$ conjecture given many years ago.

We review recent developments in two-dimensional ${𝒩}=(2,2)$ supersymmetric gauge theories focusing on the implementation and applications of localization techniques.

The calculation of $H\to \gamma \gamma$ displays interesting behavior which depends on the regulator used in the integration over loop momenta. If calculated using a gauge-invariant regulator, such as dimensional regularization, the calculation yields a unique, finite, gauge-invariant result. If four-dimensional symmetric regulation is used without finite subtractions, additional pieces occur which spoil QED gauge invariance. In both cases, a finite result is obtained, but the particular finite result depends on the regulator utilized in the calculation.

While gauge-invariant regulators such as dimensional regularization are normally used, four-dimensional symmetric integration is also physically motivated. Also, the gauge-invariance-violating terms that arise using four-dimensional symmetric integration are of the same form for the fermionic, scalar, and the SM $W^{\pm }$ loop calculated in renormalizable gauge. This presents an interesting possibility. Inspired by anomaly cancellation, we ask if it is possible that these gauge-invariance-violating terms may cancel in certain models when contributions from all diagrams are included.

Here, we calculate the regulator-dependent contributions to $H\to \gamma \gamma$ arising from generic fermion and scalar loops, as well as the Standard Model $W^{\pm }$ loop contribution, which we evaluate in renormalizable gauge for general $\xi$. We find that a cancellation between such terms is possible, and derive the cancellation condition. Additionally, we find that this cancellation condition ensures QED gauge invariance without finite subtractions for any regulator used, not just for four-dimensional symmetric integration.

We additionally relate the regulator-dependent terms in $H\to \gamma \gamma$ to the behavior of quadratically-divergent Higgs tadpole diagrams under shifts of internal loop momentum. Thus, the cancellation condition for the gauge-invariance-violating terms in $H\to \gamma \gamma$ implies a relation between the quadratic divergences in Higgs tadpole diagrams; this has consequences for hypothesized solutions to the hierarchy problem. Lastly, we find that the MSSM obeys our cancellation condition.

This paper studies the quantum modifications of the Reissner–Nordström–(A)dS black hole within Quantum Einstein Gravity, coupled to an electromagnetic sector. Quantum effects are introduced on the level of the improvements of the classical solution, where the originally constant couplings ($G_0$, ${\mathrm{\Lambda }}_0$ and ${\alpha }_0$) are promoted to scale dependent quantities ($G_k$, ${\mathrm{\Lambda }}_k$ and ${\alpha }_k$). Those running couplings are calculated in the functional renormalization group approach. A crucial point of this so-called “improving solutions” procedure is the scale setting where the arbitrary scale $k$ acquires physical meaning due to a relation to the coordinate scale $r$. It is proposed to use such scale settings which are stable after iterative improvements. Using this method one finds that for those improved solutions, there is no stable remnant and due to the appearance of a new internal horizon, there is also no necessity to impose a minimal black hole mass for charged black holes, in order to avoid the cosmic censorship hypothesis.

The $\mathrm{{\rm Y}}(nS)\to B_c^{\ast }D$ weak decays $(n=1,2,3)$ are investigated with perturbative QCD approach. It is found that the CKM-favored $\mathrm{{\rm Y}}(nS)\to B_c^{\ast }{D}_s$ decays have branching ratio of ${𝒪}(10^{-10})$, which might be potentially accessible to the future LHC and SuperKEKB experiments.

In this paper, we extend the Gribov–Zwanziger framework accounting for the existence of Gribov copies to the mass deformed Bagger–Lambert–Gustavsson (BLG) theory in ${𝒩}=1$ superspace. The restriction of the domain of integration in the Euclidean functional integral to the first Gribov horizon is implemented, by adding a nonlocal horizon term to the effective action. Furthermore, the soft breaking of the BRST symmetry due to horizon term is restored with the help of external sources. We compute the various Ward identities for this theory relying on the Lie 3-algebras.

We investigate Abelian and monopole contributions to spatial string tension in the deconfined phase of finite temperature SU(2) gauge theory without imposing any gauge fixing conditions. Lattice calculations of non-Abelian and Abelian spatial string tensions from the Wilson action at gauge coupling $\beta =2.74$ and lattice volume $24^3\times N_t$ $(N_t=\{24,8,6,4,2\})$ show that these string tensions agree with each other within error bars at any adopted value of $N_t$, which implies Abelian dominance. From measurements of non-Abelian, Abelian and monopole forces that arise from the corresponding spatial string tension, furthermore, we find the tendency that the monopole contribution to the spatial string tension can be almost as large as the non-Abelian and Abelian ones. The temperature dependence of the calculated non-Abelian and Abelian spatial string tensions allows us to conclude that the concept of dimensional reduction holds both for non-Abelian and Abelian sectors at temperatures higher than twice the critical temperature.

The gauge invariance analysis of theories described in noncommutative (NC) space–times can lead us to interesting results since noncommutativity is one of the possible paths to investigate quantum effects in classical theories such as general relativity, for example. This theoretical possibility has motivated us to analyze the gauge invariance of the NC version of the Proca model, which is a second-class system, in Dirac’s classification, since its classical formulation (commutative space–time) has its gauge invariance broken thanks to the mass term. To obtain such gauge invariant model, we have used the gauge unfixing method to construct a first-class NC version of the Proca model. We have also questioned if the gauge symmetries of NC theories are affected necessarily or not by the NC parameter. In this way, we have calculated its respective symmetries in a standard way via Poisson brackets.

The ATLAS and CMS Collaborations of the Large Hadron Collider (LHC) have reported an excess of events in diphoton channel with invariant mass of about 750 GeV. With low energy supersymmetry breaking, we systematically consider the sgoldstino scalar S as the new resonance, which is a linear combination of the CP-even scalar $s$ and CP-odd pseudoscalar $a$. Because we show that $s$ and $a$ can be degenerated or have large mass splitting, we consider two cases for all the following three scenarios: (1) Single resonance, $s$ is the 750 GeV resonance decays to a pair of 1 GeV pseudoscalar $a$ with suitable decay length, these two $a$ decay into collimated pair of photons which cannot be distinguished at the LHC and may appear as diphotons instead of four photons. (2) Twin resonances, $m_s\simeq m_a$ with a mass difference of about 40 GeV and both $s$ and $a$ decay into diphoton pairs. For productions, we consider three scenarios: (I) vector-boson fusion; (II) gluon–gluon fusion; (III) $q\bar{q}$ pair production. In all these scenarios with two kinds of resonances, we find the parameter space that satisfies the diphoton production cross-section from 3 to 13 fb and all the other experimental constraints. And we address the decay width as well. In particular, in the third scenario, we observe that the production cross-section is small but the decay width of $s$ or $a$ can be from 40 to 60 GeV. Even if the 750 GeV diphoton excesses were not confirmed by the ATLAS and CMS experiments, we point out that our proposal can be used to explain the current and future diphoton excesses.

Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles naturally. The application of Grassmannian duality cuts down the number of states substantially and is vital for constructing sensible Lagrangians anyhow. We apply duality to all of the subgroups within the classification group $\mathrm{\text{SU}}(3)\times \mathrm{\text{SU}}{(2)}_L\times \mathrm{\text{SU}}{(2)}_R$, which encompasses the standard model gauge group, and thereby determine the full state inventory; this includes the definite prediction of quarks with charge $-4/3$ and other exotic states. Assuming universal gravitational coupling to the gauge fields and parity even property curvature, we also obtain $4{sin}^2{𝜃}_w=1-2\alpha /3{\alpha }_s$ which is not far from the experimental value around the $M_Z$ mass.