In this paper we study the effects of a nonzero chemical potential in $(1+1)$-dimensional quantum field models at finite temperature. We particularly consider massless fermions in an Abelian gauge field background and calculate the effective action by evaluating the $n$-point functions. We find that the structure of the amplitudes corresponds to a generalization of the structure noted earlier in a calculation without a chemical potential (the associated integrals carry the dependence on the chemical potential). Our calculation shows that the chiral anomaly is unaffected by the presence of a chemical potential at finite temperature. However, unlike in the absence of a chemical potential, odd point functions do not vanish. We trace this to the fact that in the presence of a chemical potential the generalized charge conjugation symmetry of the theory allows for such amplitudes. In fact, we find that all the even point functions are even functions of $\mu$, while the odd point functions are odd functions of $\mu$ which is consistent with this generalized charge conjugation symmetry. We show that the origin of the structure of the amplitudes is best seen from a formulation of the theory in terms of left- and right-handed spinors. The calculations are also much simpler in this formulation and it clarifies many other aspects of the theory.

We consider QCD-like theories with one massless fermion in various representations of the gauge group $\mathrm{SU}(N)$. The theories are formulated on $R_3\times S_1$. In the decompactification limit of large $r(S_1)$ all these theories are characterized by confinement, mass gap, and spontaneous breaking of a (discrete) chiral symmetry ($\chi \mathrm{SB}$). At small $r(S_1)$, in order to stabilize the vacua of these theories at a center-symmetric point, we suggest to perform a double-trace deformation. With this deformation, the theories at hand are at weak coupling at small $r(S_1)$ and yet exhibit basic features of the large $r(S_1)$ limit: confinement and $\chi \mathrm{SB}$. We calculate the string tension, mass gap, bifermion condensates, and $\theta$ dependence. The double-trace deformation becomes dynamically irrelevant at large $r(S_1)$. Despite the fact that at small $r(S_1)$ confinement is Abelian, while it is expected to be non-Abelian at large $r(S_1)$, we argue that small and large $r(S_1)$ physics are continuously connected. If so, one can use small $r(S_1)$ laboratory to extract lessons about QCD and QCD-like theories on $R_4$.

Modifications to gravity that add additional functions of the Ricci curvature to the Einstein-Hilbert action—collectively known as $f(R)$ theories—have been studied in great detail. When considered as complete theories of gravity they can generate nonperturbative deviations from the general relativistic predictions in the solar system, and the simplest models show instabilities on cosmological scales. Here, we show that it is possible to treat $f(R)=R\pm {\mu }^4/R$ gravity in a perturbative fashion such that it shows no instabilities on cosmological scales and, in the solar system, is consistent with measurements of the parametrized post-Newtonian parameters. We show that such a theory produces a spatially flat, accelerating universe, even in the absence of dark energy and when the matter density is too small to close the Universe in the general relativistic case.

In this paper we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved space-time. The nonrelativistic quantum dynamics are investigated using the Foldy-Wouthuysen expansion. The gravitational Aharonov-Casher and He-McKellar-Wilkens effects are investigated for a series of electric and magnetic field configurations.

Many models of high-energy physics possess metastable vacua. It is conceivable that the Universe can get trapped in such a false vacuum, irrespective of its origin and prior history, at an earlier stage during its evolution. The ensuing false vacuum inflation results in a cold and empty universe and has a generic graceful exit problem. We show that an inflection point inflation along the flat directions of the minimal supersymmetric standard model (MSSM) can resolve this graceful exit problem by inflating the bubble, which nucleates out of a false vacuum. The important point is that the initial condition for an MSSM inflation can be naturally realized, due to an attractor behavior toward the inflection point. We investigate these issues in detail and also present an example where metastable vacua, hence the false vacuum inflation, can happen within the MSSM.

Data from a network of gravitational-wave detectors can be analyzed in coincidence to increase detection confidence and reduce nonstationarity of the background. We propose and explore a geometric algorithm to combine the data from a network of detectors. The algorithm makes optimal use of the variances and covariances that exist among the different parameters of a signal in a coincident detection of events. The new algorithm essentially associates with each trigger ellipsoidal regions in parameter space defined by the covariance matrix. Triggers from different detectors are deemed to be in coincidence if their ellipsoids have a nonzero overlap. Compared to an algorithm that uses uncorrelated windows separately for each of the signal parameters, the new algorithm greatly reduces the background rate thereby increasing detection efficiency at a given false alarm rate.

The motion of a $\mathrm{D}p$-brane in the background of a stack of coincident NS5-branes is analyzed as the motion of a relativistic point particle in the transverse space of the five-branes. In this system, the particle experiences a proper acceleration orthogonal to its proper velocity due to the background dilaton field which changes the dynamics from that of a simple geodesic motion. In particular, we show that in the vicinity of the five-branes, it is this acceleration which is responsible for modifying the motion of the radial mode to that of an inverted simple harmonic oscillator leading to the tachyonic instability.

We consider the direct and indirect detection signatures of weakly interacting massive particles (WIMPs) ${\chi }^0$ in kinematic regimes with a heavier, but nearly degenerate, charged state ${\chi }^{\pm }$. For small splittings of $\mathcal{O}(10)\mathrm{MeV}$, the scattering of WIMPs off nuclei may be dominated by inelastic recombination processes mediated by the formation of (${\chi }^{-}N$) bound states, leading to a distinct signature for direct detection. These cross sections are bound primarily by limits on the abundance of heavy isotopes, and may be considerably larger than the elastic scattering cross section in more conventional models. If the mass splitting is too large for recombination to occur, there may still be a significant resonant enhancement of loop-induced electromagnetic form factors of the WIMP, which can enhance the elastic scattering cross section. We also discuss how this regime affects the annihilation cross section and indirect detection signatures, and note the possibility of a significant mono-energetic $\gamma$ signal, mediated by resonant processes near the (${\chi }^{+}{\chi }^{-}$) bound-state threshold.

We calculate the nucleon sigma term in two-flavor lattice QCD utilizing the Feynman-Hellman theorem. Both sea and valence quarks are described by the overlap fermion formulation, which preserves exact chiral and flavor symmetries on the lattice. We analyze the lattice data for the nucleon mass using the analytical formulae derived from the baryon chiral perturbation theory. From the data at valence quark mass set different from sea quark mass, we may extract the sea quark contribution to the sigma term, which corresponds to the strange quark content. We find that the strange quark content is much smaller than the previous lattice calculations and phenomenological estimates.

In recent work, the Schwarzschild interior of a black hole was investigated, incorporating quantum gravitational modifications due to loop quantum gravity. The central Schwarzschild singularity was shown to be replaced by a Nariai type universe. In this brief report we show that this interior solution is stable with respect to small perturbations, in contrast to the classical Nariai universe.

We consider a cosmological solution which can explain anisotropic evolution of spatial dimensions and the stabilization of extra dimensions in brane gas formalism. We evaluate the effective potentials, induced by brane gas, bulk flux and supergravity particles, which govern the sizes of the observed three and the extra dimensions. It is possible that the wrapped internal volume can oscillate between two turning points or sit at the minimum of the potential while the unwrapped three-dimensional volume can expand monotonically. Including the supergravity particles makes the effective potential steeper as the internal volume shrinks.

Motivated by a desire to shed light on the strong-coupling behavior of dimensions of short gauge-theory operators, we consider the famous example of folded spinning string in ${\mathrm{AdS}}_5$ in the limit of small semiclassical spin parameter $\mathcal{S}=\frac{S}{\sqrt{\lambda }}$. In this limit the string becomes short and is moving in a near-flat central region of ${\mathrm{AdS}}_5$. Its energy scales with spin as $E=\sqrt{2S}[a_0+a_{1}S+a_2{S}^2+\dots ]$. We explicitly compute the leading 1-loop quantum ${\mathrm{AdS}}_5\times S^5$ superstring correction to the short string energy and show that the coefficient $a_0$ is not renormalized from its classical value while $a_1$ receives a nontrivial contribution containing $\zeta (3)$.

Conformal invariance for bosonic strings in time-dependent backgrounds of graviton, dilaton, and Kalb-Ramond field is obtained by imposing Weyl-beta functions to be homogeneous in time, to all orders in ${\alpha }^{\prime }$. This construction is possible in any target-space dimension, as a result of the nontrivial background configurations. The electromagnetic effects of the antisymmetric-tensor field, when coupled to an Abelian (electromagnetic) gauge field, are discussed in the framework of a four-dimensional Minkowski universe, for concreteness. Nontrivial optical activity is demonstrated, which constitutes a way of detecting string-inspired axion/dilaton effects in such models.

We consider extremal black hole attractors [both Bogomol’nyi-Prasad-Sommerfield (BPS) and non-BPS] for $\mathcal{N}=3$ and $\mathcal{N}=5$ supergravity in $d=4$ space-time dimensions. Attractors for matter-coupled $\mathcal{N}=3$ theory are similar to attractors in $\mathcal{N}=2$ supergravity minimally coupled to Abelian vector multiplets. On the other hand, $\mathcal{N}=5$ attractors are similar to attractors in $\mathcal{N}=4$ pure supergravity, and in such theories only $\frac{1}{\mathcal{N}}$-BPS nondegenerate solutions exist. All the above-mentioned theories have a simple interpretation in the first order (fake supergravity) formalism. Furthermore, such theories do not have a $d=5$ uplift. Finally we comment on the duality relations among the attractor solutions of $\mathcal{N}\ge 2$ supergravities sharing the same full bosonic sector.

We propose a twisted supersymmetric (SUSY) invariant formulation of the Chern-Simons theory on a Euclidean three-dimensional lattice. The SUSY algebra to be realized on the lattice is the $N=4$ $D=3$ twisted algebra that was recently proposed by D’Adda et al. In order to keep the manifest anti-Hermiticity of the action, we introduce oppositely oriented supercharges. Accordingly, the naive continuum limit of the action formally corresponds to the Landau-gauge fixed version of the Chern-Simons theory with complex gauge group which was originally proposed by Witten. We also show that the resulting action consists of parity even and odd parts with different coefficients.

We propose an all orders beta function for ordinary Yang-Mills theories with or without fermions inspired by the Novikov-Shifman-Vainshtein-Zakharov beta function of $\mathcal{N}=1$ supersymmetric gauge theories. The beta function allows us to bound the conformal window. When restricting to one adjoint Weyl fermion we show how the proposed beta function matches the one of supersymmetric Yang-Mills theory. The running of the pure Yang-Mills coupling is computed and the deviation from the two loop result is presented. We then compare the deviation with the one obtained from lattice data also with respect to the two loop running.

We study the polarization of the vacuum for a scalar field, $⟨{\varphi }^2⟩$, on a asymptotically anti-de Sitter black hole geometry. The method we follow uses the WKB analytic expansion and point-splitting regularization, similar to previous calculations in the asymptotically flat case. Following standard procedures, we write the Green function, regularize the initial divergent expression by point-splitting, renormalize it by subtracting geometrical counterterms, and take the coincidence limit in the end. After explicitly demonstrating the cancellation of the divergences and the regularity of the Green function, we express the result as a sum of two parts. One is calculated analytically and the result is expressed in terms of some generalized zeta functions, which appear in the computation of functional determinants of Laplacians on Riemann spheres. We also describe some systematic methods to evaluate these functions numerically. Interestingly, the WKB approximation naturally organizes $⟨{\varphi }^2⟩$ as a series in such zeta functions. We demonstrate this explicitly up to next-to-leading order in the WKB expansion. The other term represents the “remainder” of the WKB approximation and depends on the difference between an exact (numerical) expression and its WKB counterpart. This has to be dealt with by means of numerical approximation. The general results are specialized to the case of Schwarzschild-anti-de Sitter black hole geometries. The method is efficient enough to solve the semiclassical Einstein’s equations taking into account the backreaction from quantum fields on asymptotically anti-de Sitter black holes.

In inflationary cosmological models driven by an inflaton field the origin of the primordial inhomogeneities which are responsible for large-scale structure formation are the quantum fluctuations of the inflaton field. These are usually calculated using the standard theory of cosmological perturbations, where both the gravitational and the inflaton fields are linearly perturbed and quantized. The correlation functions for the primordial metric fluctuations and their power spectrum are then computed. Here we introduce an alternative procedure for calculating the metric correlations based on the Einstein-Langevin equation which emerges in the framework of stochastic semiclassical gravity. We show that the correlation functions for the metric perturbations that follow from the Einstein-Langevin formalism coincide with those obtained with the usual quantization procedures when the scalar field perturbations are linearized. This method is explicitly applied to a simple model of chaotic inflation consisting of a Robertson-Walker background, which undergoes a quasi-de Sitter expansion, minimally coupled to a free massive quantum scalar field. The technique based on the Einstein-Langevin equation can, however, deal naturally with the perturbations of the scalar field even beyond the linear approximation, as is actually required in inflationary models which are not driven by an inflaton field, such as Starobinsky’s trace-anomaly driven inflation or when calculating corrections due to nonlinear quantum effects in the usual inflaton driven models.

Canonical gravity in real Ashtekar-Barbero variables is generalized to allow for fermionic matter. The resulting torsion changes several expressions in Holst’s original vacuum analysis, which are summarized here. This in turn requires adaptations to the known loop quantization of gravity coupled to fermions, which is discussed on the basis of the classical analysis. As a result, parity invariance is not manifestly realized in loop quantum gravity.

We analyze the loop quantization of the family of vacuum Bianchi I spacetimes, a gravitational system of which classical solutions describe homogeneous anisotropic cosmologies. We rigorously construct the operator that represents the Hamiltonian constraint, showing that the states of zero volume completely decouple from the rest of quantum states. This fact ensures that the classical cosmological singularity is resolved in the quantum theory. In addition, this allows us to adopt an equivalent quantum description in terms of a well-defined densitized Hamiltonian constraint. This latter constraint can be regarded in a certain sense as a difference evolution equation in an internal time provided by one of the triad components, which is polymerically quantized. Generically, this evolution equation is a relation between the projection of the quantum states in three different sections of constant internal time. Nevertheless, around the initial singularity the equation involves only the two closest sections with the same orientation of the triad. This has a double effect: on the one hand, physical states are determined just by the data on one section, on the other hand, the evolution defined in this way never crosses the singularity, without the need of any special boundary condition. Finally, we determine the inner product and the physical Hilbert space employing group averaging techniques, and we specify a complete algebra of Dirac observables. This completes the quantization program.