A new technique is explored for the Monte Carlo sampling of complex-valued distributions. The method is based on a heat bath approach where the conditional probability is replaced by a positive representation of it on the complex plane. Efficient ways to construct such representations are also introduced. The performance of the algorithm is tested on small and large lattices with a $\lambda {\varphi }^4$ theory with quadratic nearest-neighbor complex coupling. The method works for moderate complex couplings, reproducing reweighting and complex Langevin results and fulfilling various Schwinger-Dyson relations.

In the light of the recent result from KamLAND-Zen (KLZ) and GERDA Phase-II, we update the bounds on the effective mass and the new physics parameters, relevant for neutrinoless double beta decay ($0\nu \beta \beta$). In addition to the light Majorana neutrino exchange, we analyze beyond standard model contributions that arise in left-right symmetry and R-parity violating supersymmetry. The improved limit from KLZ constrains the effective mass of light neutrino exchange down to sub-eV mass regime 0.06 eV. Using the correlation between the ${}^{136}\mathrm{Xe}$ and ${}^{76}\mathrm{Ge}$ half-lives, we show that the KLZ limit individually rules out the positive claim of observation of $0\nu \beta \beta$ for all nuclear matrix element compilation. For the left-right symmetry and R-parity violating supersymmetry, the KLZ bound implies a factor of 2 improvement of the effective mass and the new physics parameters. The future ton scale experiments such as, nEXO will further constrain these models, in particular, will rule out standard as well as Type-II dominating LRSM inverted hierarchy scenario.

We determine the anomalous dimensions of baryon operators for the three-color theory as functions of the number of massless flavors within the conformal window to the maximum known order in perturbation theory. We show that the anomalous dimension of the baryon is controllably small, within the $\delta$ expansion, for a wide range of number of flavors. We also find that this is always smaller than the anomalous dimension of the fermion mass operator. These findings challenge the partial compositeness paradigm.

By introducing interacting scalar fields, we tried to engineer physically motivated holographic phase diagrams which may be interesting in the context of various known condensed matter systems. We introduce an additional scalar field in the bulk which provides a tunable parameter in the boundary theory. By exploiting the way the tuning parameter changes the effective masses of the bulk interacting scalar fields, desired phase diagrams can be engineered for the boundary order parameters dual to those scalar fields. We give a few examples of generating phase diagrams with phase boundaries which are strikingly similar to the known quantum phases at low temperature such as the superconducting phases. However, the important difference is that all the phases we have discussed are characterized by neutral order parameters. At the end, we discuss if there exists any emerging scaling symmetry associated with a quantum critical point hidden under the dome in this phase diagram.

In the context of studying the 4D-effective potentials of type IIB nongeometric flux compactifications, this article has a twofold goal. First, we present a modular invariant symplectic rearrangement of the tree level nongeometric scalar potential arising from a flux superpotential which includes the S-dual pairs of nongeometric fluxes ($Q$, $P$), the standard NS-NS and RR three-form fluxes ($F_3$, $H_3$), and the geometric flux ($\omega$). This “symplectic formulation” is valid for arbitrary numbers of Kähler moduli, and the complex structure moduli which are implicitly encoded in a set of symplectic matrices. In the second part, we further explicitly rewrite all the symplectic ingredients in terms of saxionic and axionic components of the complex structure moduli. The same leads to a compact form of the generic scalar potential being explicitly written out in terms of all the real moduli/axions. Moreover, the final form of the scalar potential needs only the knowledge of some topological data (such as Hodge numbers and the triple-intersection numbers) of the compactifying threefolds and their respective mirrors. Finally, we demonstrate how the same is equivalent to say that, for a given concrete example, various pieces of the scalar potential can be directly read off from our generic proposal, without the need of starting from the Kähler and superpotentials.

We study bosonization in $2+1$ dimensions using mirror symmetry, a duality that relates pairs of supersymmetric theories. Upon breaking supersymmetry in a controlled way, we dynamically obtain the bosonization duality that equates the theory of a free Dirac fermion to QED3 with a single scalar boson. This duality may be used to demonstrate the bosonization duality relating an $O(2)$-symmetric Wilson-Fisher fixed point to QED3 with a single Dirac fermion, Peskin-Dasgupta-Halperin duality, and the recently conjectured duality relating the theory of a free Dirac fermion to fermionic QED3 with a single flavor. Chern-Simons and BF couplings for both dynamical and background gauge fields play a central role in our approach. In the course of our study, we describe a “chiral” mirror pair that may be viewed as the minimal supersymmetric generalization of the two bosonization dualities.

We discuss a possible extension of calculations of the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime to a nonasymptotically flat case. We examine a relation between the bending angle of light and the Gauss-Bonnet theorem by using the optical metric. A correspondence between the deflection angle of light and the surface integral of the Gaussian curvature may allow us to take account of the finite distance from a lens object to a light source and a receiver. Using this relation, we propose a method for calculating the bending angle of light for such cases. Finally, this method is applied to two examples of the nonasymptotically flat spacetimes to suggest finite-distance corrections: the Kottler (Schwarzschild–de Sitter) solution to the Einstein equation and an exact solution in Weyl conformal gravity.

We propose a mechanism to generate a nearly scale-invariant spectrum of adiabatic scalar perturbations about a stable, ekpyrotic background. The key ingredient is a coupling between a single ekpyrotic field and a perfect fluid of ultrarelativistic matter. This coupling introduces a friction term into the equation of motion for the field, opposing the Hubble antifriction, which can be chosen such that an exactly scale-invariant (or nearly scale-invariant) spectrum of adiabatic density perturbations is continuously produced throughout the ekpyrotic phase. This mechanism eliminates the need for a second (entropic) scalar field and hence any need for introducing a second phase for converting entropic into curvature fluctuations. It also reduces the constraints on the equation of state during the ekpyrotic phase and, thereby, the need for parametric fine-tuning.

We investigate a bounce inflation model with a graceful exit into the Friedmann-Robertson-Walker (FRW) decelerated Universe within $f(T)$-gravity framework, where $T$ is the torsion scalar in the teleparallelism. We study the cosmic thermal evolution, the model predicts a supercold universe during the precontraction phase, which is consistent with the requirements of the slow-roll models, while it performs a reheating period by the end of the contraction with a maximum temperature just below the grand unified theory (GUT) temperature. However, it matches the radiation temperature of the hot big bang at later stages. The equation-of-state due to the effective gravitational sector suggests that our Universe is self-accelerated by teleparallel gravity. We assume the matter component to be a canonical scalar field. We obtain the scalar field potential that is induced by the $f(T)$ theory. The power spectrum of the model is nearly scale invariant. In addition, we show that the model unifies inflaton and quintessence fields in a single model. Also, we revisited the primordial fluctuations in $f(T)$ bounce cosmology, to study the fluctuations that are produced at the precontraction phase.

Recently, we numerically showed that, for a nonminimal coupling that is a simple power of the scale factor, scale invariant magnetic fields arise in a class of bouncing universes. In this work, we analytically evaluate the spectrum of magnetic and electric fields generated in a subclass of such models. We illustrate that, for cosmological scales which have wave numbers much smaller than the wave number associated with the bounce, the shape of the spectrum is preserved across the bounce. Using the analytic solutions obtained, we also illustrate that the problem of backreaction is severe at the bounce. Finally, we show that the power spectrum of the magnetic field remains invariant under a two-parameter family of transformations of the nonminimal coupling function.

We determine the effect of intergalactic magnetic fields on the distribution of high-energy gamma rays by performing three-dimensional Monte Carlo simulations of the development of gamma-ray-induced electromagnetic cascades in the magnetized intergalactic medium. We employ the so-called “Large Sphere Observer” method to efficiently simulate blazar gamma ray halos. We study magnetic fields with a Batchelor spectrum and with maximal left- and right-handed helicities. We also consider the case of sources whose jets are tilted with respect to the line of sight. We verify the formation of extended gamma ray halos around the source direction, and observe spiral-like patterns if the magnetic field is helical. We apply the $Q$-statistics to the simulated halos to extract their spiral nature and also propose an alternative method, the $S$-statistics. Both methods provide a quantitative way to infer the helicity of the intervening magnetic fields from the morphology of individual blazar halos for magnetic field strengths $B\gtrsim {10}^{-15}\mathrm{G}$ and magnetic coherence lengths $L_{\mathrm{c}}\gtrsim 100\mathrm{Mpc}$. We show that the $S$-statistics has a better performance than the $Q$-statistics when assessing magnetic helicity from the simulated halos.

We propose that the vacuum state of a scalar field around a black hole is a modified Unruh vacuum. In ($1+1$) dimensions, we show that a free-faller close to such an horizon can be modeled as an inertial observer in a modified Minkowski vacuum. The modification allows for information-leaking correlations at high frequencies. Using a Gaussian detector centered at $k_0$, we find that the expectation value of the number operator for a detector crossing the horizon is proportional to $1/|k_0|$, implying that the free-faller will observe unbounded numbers of high-energy photons, i.e. a firewall.

We investigate the effect of turning on temperature for the charge neutral phase of two-flavor color superconducting (2SC) dense quark matter in the presence of constant external magnetic field. Within the Nambu–Jona-Lasinio model, by tuning the diquark coupling strength, we study the interdependent evolution of the quark Bardeen-Cooper-Schrieffer gap and dynamical mass as functions of temperature and magnetic field. We find that magnetic field $B\gtrsim 0.02{\mathrm{GeV}}^2$ ($10^{18}\mathrm{G}$) leads to anomalous temperature behavior of the gap in the gapless 2SC phase (moderately strong coupling), reminiscent of previous results in the literature found in the limit of weak coupling without magnetic field. The 2SC gap in the strong coupling regime is abruptly quenched at ultrahigh magnetic field due to the mismatched Fermi surfaces of up and down quarks imposed by charge neutrality and oscillation of the gap due to Landau level quantization. The dynamical quark mass also displays strong oscillation and magnetic catalysis at high magnetic field, although the latter effect is tempered by nonzero temperature. We discuss the implications for newly born compact stars with superconducting quark cores.

We present a detailed phenomenological study of $Z$-boson production in association with a jet through next-to-next-to-leading order (NNLO) in perturbative QCD. Fiducial cross sections and differential distributions for both 8 TeV and 13 TeV LHC collisions are presented. We study the impact of different parton distribution functions (PDFs) on predictions for the $Z+\mathrm{jet}$ process. Upon inclusion of the NNLO corrections, the residual scale uncertainty is reduced such that both the total rate and the transverse momentum distributions can be used to discriminate between various PDF sets.

We study the longitudinal-transverse double-spin asymmetry with a $\cos {\varphi }_S$ modulation in semi-inclusive deep inelastic scattering for charged and neutral pion production. We consider the particular case in which the transverse momentum of the final-state hadron is integrated out. The corresponding asymmetry may be contributed by two parts: one is the convolution of the twist-3 distribution function $g_T(x)$ and the unpolarized fragmentation function $D_1(z)$; the other is related to the coupling of the transversity distribution function $h_1(x)$ and the collinear twist-3 fragmentation function $\tilde{E}(z)$. We take into account both contributions to predict the $\cos {\varphi }_S$ asymmetry at the kinematics of CLAS12 and a future Electron Ion Collider. We find that the asymmetry of pion production at CLAS12 is sizable, and $\tilde{E}(z)$ can play an important role in the asymmetry in the large-$z$ region.

Actual solutions of the Bethe-Salpeter equation for a two-fermion bound system are becoming available directly in Minkowski space, by virtue of a novel technique, based on the so-called Nakanishi integral representation of the Bethe-Salpeter amplitude and improved by expressing the relevant momenta through light-front components, i.e. $k^{\pm }=k^0\pm k^3$. We solve a crucial problem that widens the applicability of the method to real situations by providing an analytically exact treatment of the singularities plaguing the two-fermion problem in Minkowski space, irrespective of the complexity of the irreducible Bethe-Salpeter kernel. This paves the way for feasible numerical investigations of relativistic composite systems, with any spin degrees of freedom. We present a thorough comparison with existing numerical results, evaluated in both Minkowski and Euclidean space, fully corroborating our analytical treatment, as well as fresh light-front amplitudes illustrating the potentiality of non perturbative calculations performed directly in Minkowski space.

The Higgs boson mass and top quark mass imply that the Higgs quartic coupling vanishes around the scale of ${10}^9–{10}^{13}\mathrm{GeV}$, depending on the precise value of the top quark mass. The vanishing quartic coupling can be naturally addressed if the Higgs field originates from a five-dimensional gauge field and the fifth dimension is compactified at the scale of the vanishing Higgs quartic coupling, which is a scenario based on gauge-Higgs unification. We present a general prediction of the scenario on the proton decay process $p\to {\pi }^0{e}^{+}$. In many gauge-Higgs unification models, the first-generation fermions are localized towards an orbifold fixed point in order to realize the realistic Yukawa couplings. Hence, four-fermion operators responsible for the proton decay can appear with a suppression of the five-dimensional Planck scale (not the four-dimensional Planck scale). Since the five-dimensional Planck scale is connected to the compactification scale, we have a correlation between the proton partial decay width and the top quark mass. We show that the future Hyper-Kamiokande experiment may discover the proton decay if the top quark pole mass is larger than about 172.5 GeV.

In the first part of this paper, we calculate the disk-level $S$-matrix elements of one Ramond-Ramond (RR), one Neveu-Schwarz-Neveu-Schwarz (NSNS), and one Neveu-Schwarz (NS) vertex operator, and show that they are consistent with the amplitudes that have been recently found by applying various Ward identities. We show that the massless poles of the amplitude at low energy are fully consistent with the known $D$-brane couplings at order ${\alpha }^{\prime 2}$ that involve one RR or NSNS and two NS fields. Subtracting the massless poles, we then find the contact terms of one RR, one NSNS and one NS fields at order ${\alpha }^{\prime 2}$. Some of these terms are reproduced by the Taylor expansion and the pullback of two closed string couplings; some other couplings are reproduced by the linear graviton in the second fundamental form and by the $B$-field in the gauge field extension $F\to F+B$, in one closed and two open string couplings. In the second part, we write all of the independent covariant contractions of one RR, one NSNS, and one NS fields with unknown coefficients. We then constrain the couplings to be consistent with the linear $T$ duality and with the above contact terms. Interestingly, we have found that up to total derivative terms and Bianchi identities, these constraints uniquely fix all the unknown coefficients.