In this paper we propose a method to study the functional renormalization group (FRG) at finite chemical potential. The method consists of mapping the FRG equations within the Fermi surface into a differential equation defined on a rectangle with zero boundary conditions. To solve this equation we use an expansion of the potential in a harmonic basis. With this method we determined the phase diagram of a simple Yukawa-type model; as expected, the bosonic fluctuations decrease the strength of the transition.

We develop scattering theory in a noncommutative space defined by an $su(2)$ coordinate algebra. By introducing a positive operator valued measure as a replacement for strong position measurements, we are able to derive explicit expressions for the probability current, differential and total cross sections. We show that at low incident energies the kinematics of these expressions is identical to that of commutative scattering theory. The consequences of spatial noncommutativity are found to be more pronounced at the dynamical level where, even at low incident energies, the phase shifts of the partial waves can deviate strongly from commutative results. This is demonstrated for scattering from a spherical well. The impact of noncommutativity on the well’s spectrum and on the properties of its bound and scattering states are considered in detail. It is found that for sufficiently large well depths the potential effectively becomes repulsive and that the cross section tends towards that of hard sphere scattering. This can occur even at low incident energies when the particle’s wavelength inside the well becomes comparable to the noncommutative length scale.

The motion of a particle near a horizon of a spherically symmetric static black hole is shown to possess a universal Lyapunov exponent of chaos bounded by its surface gravity. To probe the horizon, we introduce an electromagnetic or scalar force to the particle so that it does not fall into the horizon. There appears an unstable maximum of the total potential where the evaluated maximal Lyapunov exponent is found to be to the surface gravity of the black hole. This value is independent of the external forces, the particle mass and background geometry, and in this sense this Lyapunov exponent is universal. Unless there are other sources of chaos, the Lyapunov exponent is subject to an inequality $\lambda \le 2\pi T_{\mathrm{BH}}/\hslash$, which is identical to the bound recently discovered by Maldacena, Shenker, and Stanford.

For many years, researchers have tried to glean hints about quantum gravity from black hole thermodynamics. However, black hole thermodynamics suffers from the problem of universality—at leading order, several approaches with different microscopic degrees of freedom lead to Bekenstein-Hawking entropy. We attempt to bypass this issue by using a minimal statistical mechanical model for the horizon fluid based on the Damour-Navier-Stokes (DNS) equation. For stationary asymptotically flat black hole spacetimes in general relativity, we show explicitly that, at equilibrium, the entropy of the horizon fluid is the Bekenstein-Hawking entropy. Further, we show that, for the bulk viscosity of the fluctuations of the horizon fluid to be identical to Damour, a confinement scale exists for these fluctuations, implying quantization of the horizon area. The implications and possible mechanisms from the fluid point of view are discussed.

We obtain a perturbative solution for rotating charged black holes in five-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. We start from a small undeformed Kerr-AdS solution and use the electric charge as a perturbative parameter to build up black holes with equal-magnitude angular momenta up to fourth order. These black hole solutions are described by three parameters, the charge, horizon radius and horizon angular velocity. We determine the physical quantities of these black holes and study their dependence on the parameters of black holes and arbitrary Chern-Simons coefficient. In particular, for values of the CS coupling constant beyond its supergravity value, due to a rotational instability, counterrotating black holes arise. Also the rotating solutions appear to have vanishing angular momenta and are not manifest uniquely by their global charges.

An exact solution is obtained for the gravitational bending of light in static, spherically symmetric metrics which includes the Schwarzschild–de Sitter spacetime and also the Mannheim-Kazanas metric of conformal Weyl gravity. From the exact solution, we obtain a small-bending-angle approximation for a lens system where the source, lens, and observer are coaligned. This expansion improves previous calculations where we systematically avoid parameter ranges that correspond to nonexistent null trajectories. The linear coefficient $\gamma$ characteristic to conformal gravity is shown to contribute enhanced deflection compared to the angle predicted by general relativity for small $\gamma$.

A recently presented general procedure to find static and axially symmetric, interior solutions to the Einstein equations is extended to the stationary case, and applied to find an interior solution for the Kerr metric. The solution, which is generated by an anisotropic fluid, verifies the energy conditions for a wide range of values of the parameters, and matches smoothly to the Kerr solution, thereby representing a globally regular model describing a nonspherical and rotating source of gravitational field. In the spherically symmetric limit, our model converges to the well-known incompressible perfect fluid solution. The key stone of our approach is based on an ansatz allowing to define the interior metric in terms of the exterior metric functions evaluated at the boundary source. The physical variables of the energy-momentum tensor are calculated explicitly, as well as the geometry of the source in terms of the relativistic multipole moments.

Atom interferometry is currently developing rapidly, which is now reaching sufficient precision to motivate laboratory tests of general relativity. Thus, it is extremely significant to develop a general relativistic model for atom interferometers. In this paper, we mainly present an analytical derivation process and first give a complete vectorial expression for the relativistic interferometric phase shift in an atom interferometer. The dynamics of the interferometer are studied, where both the atoms and the light are treated relativistically. Then, an appropriate coordinate transformation for the light is performed crucially to simplify the calculation. In addition, the Bordé $ABCD$ matrix combined with quantum mechanics and the “perturbation” approach are applied to make a methodical calculation for the total phase shift. Finally, we derive the relativistic phase shift kept up to a sensitivity of the acceleration $\sim 10^{-14}{\mathrm{m}/\mathrm{s}}^2$ for a $10\text{−}\mathrm{m}$-long atom interferometer.

The Hamilton-Jacobi formalism as a powerful method is being utilized to reconsider the warm inflationary scenario, where the scalar field as the main component driving inflation interacts with other fields. Separating the context into strong and weak dissipative regimes, the goal is followed for two popular functions of $\mathrm{\Gamma }$. Applying slow-rolling approximation, the required perturbation parameters are extracted and, by comparing to the latest Planck data, the free parameters are restricted. The possibility of producing an acceptable inflation is studied where the result shows that for all cases the model could successfully suggest the amplitude of scalar perturbation, scalar spectral index, its running, and the tensor-to-scalar ratio.

A model is presented in which $\mathcal{O}(10\mathrm{TeV})$ stop masses, typically required by the Higgs boson mass in supersymmetric models, do not originate from soft supersymmetry breaking terms that would drive the Higgs mass squared parameter to large negative values but rather from the mixing with vectorlike partners. Their contribution to the Higgs mass squared parameter is reduced to threshold corrections and, thus, it is one loop suppressed compared to usual scenarios. New fermion and scalar partners of the top quark with $\mathcal{O}(10\mathrm{TeV})$ masses are predicted.

The light dark matter ($\simeq 1–30\mathrm{MeV}$) particles pair produced in electron-positron annihilation $e^{-}{e}^{+}\stackrel{\gamma }{\to }\chi \overline{\chi }$ inside the supernova core can take away the energy released in the supernova SN1987A explosion. Working within the formalism of $q$-deformed statistics [with the average value of the supernovae core temperature (fluctuating) being $T_{SN}=30\mathrm{MeV}$] and using the Raffelt’s criterion on the emissivity for any new channel $\dot{ϵ}(e^{+}{e}^{-}\to \chi \overline{\chi })\le 10^{19}\mathrm{erg}{\mathrm{g}}^{-1}{\mathrm{s}}^{-1}$, we find that as the deformation parameter $q$ changes from 1.0 (undeformed scenario) to 1.1 (deformed scenario), the lower bound on the scale $\mathrm{\Lambda }$ of the dark matter effective theory varies from $3.3\times 10^6\mathrm{TeV}$ to $3.2\times 10^7\mathrm{TeV}$ for a dark matter fermion of mass $m_{\chi }=30\mathrm{MeV}$. Using the optical depth criteria on the free streaming of the dark matter fermion, we find the lower bound on $\mathrm{\Lambda }\sim 10^8\mathrm{TeV}$ for $m_{\chi }=30\mathrm{MeV}$. In a scenario, where the dark matter fermions are pair produced in the outermost sector of the supernova core [with radius $0.9R_c\le r\le R_c$, $R_c(=10\mathrm{km})$ being the supernova core radius or the radius of protoneutron star], we find that the bound on $\mathrm{\Lambda }$ ($\sim 3\times 10^7\mathrm{TeV}$) obtained from SN cooling criteria (Raffelt’s criteria) is comparable with the bound obtained from free streaming (optical depth criterion) for light fermion dark matter of mass $m_{\chi }=10–30\mathrm{MeV}$.

We study a toy version of a grand-unified theory on the lattice: An $SU(3)$ gauge theory, which experiences a Brout-Englert-Higgs effect due to a single Higgs field in the fundamental representation. This yields a perturbative breaking pattern $SU(3)\to SU(2)$. We investigate the singlet vector channel, finding a nondegenerate and massive ground state. This is in contradistinction to the perturbative prediction of three massless and five massive vector states, even though the correlation functions of the gauge bosons exhibit a weak-coupling behavior, being almost tree-level-like. However, a combination of perturbation theory with the Fröhlich-Morchio-Strocchi mechanism, and thus passing to gauge-invariant perturbation theory, allows one to predict the physical spectrum in this channel.

Coupled Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations involving singlet quark and gluon distributions are explored by a Taylor expansion at small $x$ as two first-order partial differential equations in two variables: Bjorken $x$ and $t$ ($t=ln\frac{Q^2}{{\mathrm{\Lambda }}^2}$). The system of equations are then solved by Lagrange’s method and the method of characteristics. We obtain the proton structure function $F_2^P(x,t)$ by combining the corresponding nonsinglet and singlet structure functions with both methods. Analytical solutions for $F_2^P(x,t)$ thus obtained are compared with the recent data published by the H1 and ZEUS Collaborations as well as with NNPDF3.0 parametrization, and their compatibility is checked. Comparative analysis favors the analytical solution by Lagrange’s method; the plausible reasons behind that are also discussed.

We address the general features of event-by-event fluctuations of the multiplicity of gluons produced in the scattering of a dilute hadron off a large nucleus at high energy in the fragmentation region of the dilute hadron. We relate these fluctuations to the stochasticity of the number of quanta contained in the hadron at the time of the interaction. For simplicity, we address the ideal case in which the hadron is an onium and investigate different kinematical regimes in the rapidity and onium size. We show that at large rapidity, the multiplicity distribution exhibits an exponential tail in the large-multiplicity region, which is qualitatively consistent with the proton-nucleus data. But interestingly enough, the exponential shape is determined by confinement.

Radiative corrections to elastic electron proton scattering are analyzed in effective field theory. A new factorization formula identifies all sources of large logarithms in the limit of large momentum transfer, $Q^2\gg m_e^2$. Explicit matching calculations are performed through two-loop order. A renormalization analysis in soft-collinear effective theory is performed to systematically compute and resum large logarithms. Implications for the extraction of charge radii and other observables from scattering data are discussed. The formalism may be applied to other lepton-nucleon scattering and $e^{+}{e}^{-}$ annihilation processes.

We report the first search for the $J^{PC}=0^{--}$ glueball in $\mathrm{\Upsilon }(1S)$ and $\mathrm{\Upsilon }(2S)$ decays with data samples of $(102\pm 2)\times 10^6$ and $(158\pm 4)\times 10^6$ events, respectively, collected with the Belle detector. No significant signals are observed in any of the proposed production modes, and the 90% credibility level upper limits on their branching fractions in $\mathrm{\Upsilon }(1S)$ and $\mathrm{\Upsilon }(2S)$ decays are obtained. The inclusive branching fractions of the $\mathrm{\Upsilon }(1S)$ and $\mathrm{\Upsilon }(2S)$ decays into final states with a ${\chi }_{c1}$ are measured to be $\mathcal{B}(\mathrm{\Upsilon }(1S)\to {\chi }_{c1}+\text{anything})=(1.90\pm 0.43(\text{stat})\pm 0.14(\text{syst}))\times {10}^{-4}$ with an improved precision over prior measurements and $\mathcal{B}(\mathrm{\Upsilon }(2S)\to {\chi }_{c1}+\text{anything})=(2.24\pm 0.44(\text{stat})\pm 0.20(\text{syst}))\times {10}^{-4}$ for the first time.

We analyze the exchange of information in different cosmological backgrounds when sender and receiver are timelike separated and communicate through massless fields (without the exchange of light signals). Remarkably, we show that the dominance of a cosmological constant makes the amount of recoverable information imprinted in the field by the sender extremely resilient: it does not decay in time or with the spatial separation of the sender and receiver, and it actually increases with the rate of expansion of the Universe. This is in stark contrast with the information carried by conventional light signals and with previous results on timelike communication through massless fields in matter-dominated cosmologies.

We develop numerical tools and apply them to solve the relativistic Yang-Mills-Higgs equations in a model where the $SU(N)$ symmetry is spontaneously broken to its center. In $SU(2)$ and $SU(3)$, we obtain the different field profiles for infinite and finite center strings, with end points at external monopole sources. Exploration of parameter space permits the detection of a region where the equations get Abelianized. Finally, a general parametrization of the color structure of $SU(2)$ fields leads us to a reference point where an Abelian-like Bogomol’nyi-Prasad-Sommereld (BPS) bound is reconciled with $N$-ality.

We introduce the construction of a new framework for probing discrete emergent geometry and boundary-boundary observables based on a fundamentally a-dimensional underlying network structure. Using a gravitationally motivated action with Forman weighted combinatorial curvatures and simplicial volumes relying on a decomposition of an abstract simplicial complex into realized embeddings of proper skeletons, we demonstrate properties such as a minimal volume-scale cutoff, the necessity of a term playing the role of a positive definite cosmological constant as a regulator for nondegenerate geometries, and naturally emergent simplicial structures from Metropolis network evolution simulations with no restrictions on attachment rules or regular building blocks. We see emergent properties which echo results from both the spinfoam formalism and causal dynamical triangulations in quantum gravity, and provide analytical and numerical results to support the analogy. We conclude with a summary of open questions and intent for future work in developing the program.

The boundary Weyl anomalies live on a codimension-1 boundary, $\partial \mathcal{M}$. The entanglement entropy originates from infinite correlations on both sides of a codimension-2 surface, $\mathrm{\Sigma }$. Motivated to have a further understanding of the boundary effects, we introduce a notion of reduction entropy, which, guided by thermodynamics, is a combination of the boundary effective action and the boundary stress tensor defined by allowing the metric on $\partial \mathcal{M}$ to fluctuate. We discuss how a reduction might be performed so that the reduction entropy reproduces the entanglement structure.