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We study the evolution of the Universe at early stages, we discuss also preheating in the framework of hybrid braneworld inflation by setting conditions on the coupling constants $lambda $ and $g$ for effective production of $chi$-particles. Consider ing the phase between the time observable CMB scales crossed the horizon and the present time, we write reheating and preheating parameters $N_{re}$, $T_{re}$ and $N_{pre}$ in terms of the scalar spectral index $n_{s}$, and prove that, unlike the reheating case, the preheating duration does not depend on the values of the equation of state $omega ^{ast }$. We apply the slow-roll approximation in the high energy limit to constrain the parameters of D-term hybrid potential. We show also that some inflationary parameters, in particular, the spectral index $n_{s}$ demand that the potential parameter $alpha$ is bounded as $alpha geq 1$ to be consistent with $Planck$s data, while the ratio $r$ is in agreement with observation for $ alpha leq 1 $ considering high inflationary e-folds. We also propose an investigation of the brane tension effect on the reheating temperature. Comparing our results to recent CMB measurements, we study preheating and reheating parameters $N_{re}$, $T_{re}$ and $N_{pre}$ in the Hybrid D-term inflation model in the range $0.8leq alphaleq 1.1$, and conclude that $T_{re}$ and $N_{re}$ require $alpha leq 1$, while for $N_{pre}$ the condition $alpha leq 0.9$ must be satisfied, to be compatible with $Planck$s results.
153 - Jake Stedman 2021
In this paper we introduce a new method for generating gauged sigma models from four-dimensional Chern-Simons theory and give a unified action for a class of these models. We begin with a review of recent work by several authors on the classical gene ration of integrable sigma models from four dimensional Chern-Simons theory. This approach involves introducing classes of two dimensional defects into the bulk on which the gauge field must satisfy certain boundary conditions. By solving the equations of motion of the gauge one finds an integrable sigma models by substituting the solution back into the action. This integrability is guaranteed because the gauge field is gauge equivalent to the Lax connection of the sigma model. By considering a theory with two four-dimensional Chern-Simons fields coupled together on two dimensional surfaces in the bulk we are able to introduce new classes of `gauged defects. By solving the bulk equations of motion we find a unified action for a set of genus zero integrable gauged sigma models. The integrability of these models is guaranteed as the new coupling does not break the gauge equivalence of the gauged fields to their Lax connections. Finally, we consider a couple of examples in which we derive the gauged Wess-Zumino-Witten and Nilpotent gauged Wess-Zumino-Witten models. This latter model is of note given one can find the conformal Toda models from it.
We study supersymmetric domain walls of four dimensional $SU(N)$ SQCD with $N$ and $N+1$ flavors. In $4d$ we analyze the BPS differential equations numerically. In $3d$ we propose the $mathcal{N}=1$ Chern-Simons-Matter gauge theories living on the wa lls. Compared with the previously studied regime of $F<N$ flavors, we encounter a couple of novelties: with $N$ flavors, there are solutions/vacua breaking the $U(1)$ baryonic symmetry; with $N+1$ flavors, our $3d$ proposal includes a linear monopole operator in the superpotential.
The exact expressions for integrated maximal $U(1)_Y$ violating (MUV) $n$-point correlators in $SU(N)$ ${mathcal N}=4$ supersymmetric Yang--Mills theory are determined. The analysis generalises previous results on the integrated correlator of four su perconformal primaries and is based on supersymmetric localisation. The integrated correlators are functions of $N$ and $tau=theta/(2pi)+4pi i/g_{_{YM}}^2$, and are expressed as two-dimensional lattice sums that are modular forms with holomorphic and anti-holomorphic weights $(w,-w)$ where $w=n-4$. The correlators satisfy Laplace-difference equations that relate the $SU(N+1)$, $SU(N)$ and $SU(N-1)$ expressions and generalise the equations previously found in the $w=0$ case. The correlators can be expressed as infinite sums of Eisenstein modular forms of weight $(w,-w)$. For any fixed value of $N$ the perturbation expansion of this correlator is found to start at order $( g_{_{YM}}^2 N)^w$. The contributions of Yang--Mills instantons of charge $k>0$ are of the form $q^k, f(g_{_{YM}})$, where $q=e^{2pi i tau}$ and $f(g_{_{YM}})= O(g_{_{YM}}^{-2w})$ when $g_{_{YM}}^2 ll 1$ anti-instanton contributions have charge $k<0$ and are of the form $bar q^{|k|} , hat f(g_{_{YM}})$, where $hat f(g_{_{YM}}) = O(g_{_{YM}}^{2w})$ when $g_{_{YM}}^2 ll 1$. Properties of the large-$N$ expansion are in agreement with expectations based on the low energy expansion of flat-space type IIB superstring amplitudes. We also comment on the relation of $n$-point MUV correlators to $(n-4)$-loop contributions to the four-point correlator. In particular, we argue that it is important to ensure the $SL(2, mathbb{Z})$-covariance even in the construction of perturbative loop integrands.
Exponential expansion in Unimodular Gravity is possible even in the absence of a constant potential; {em id est} for free fields. This is at variance with the case in General Relativity.
Scattering amplitudes in quantum field theories have intricate analytic properties as functions of the energies and momenta of the scattered particles. In perturbation theory, their singularities are governed by a set of nonlinear polynomial equation s, known as Landau equations, for each individual Feynman diagram. The singularity locus of the associated Feynman integral is made precise with the notion of the Landau discriminant, which characterizes when the Landau equations admit a solution. In order to compute this discriminant, we present approaches from classical elimination theory, as well as a numerical algorithm based on homotopy continuation. These methods allow us to compute Landau discriminants of various Feynman diagrams up to 3 loops, which were previously out of reach. For instance, the Landau discriminant of the envelope diagram is a reducible surface of degree 45 in the three-dimensional space of kinematic invariants. We investigate geometric properties of the Landau discriminant, such as irreducibility, dimension and degree. In particular, we find simple examples in which the Landau discriminant has codimension greater than one. Furthermore, we describe a numerical procedure for determining which parts of the Landau discriminant lie in the physical regions. In order to study degenerate limits of Landau equations and bounds on the degree of the Landau discriminant, we introduce Landau polytopes and study their facet structure. Finally, we provide an efficient numerical algorithm for the computation of the number of master integrals based on the connection to algebraic statistics. The algorithms used in this work are implemented in the open-source Julia package Landau.jl available at https://mathrepo.mis.mpg.de/Landau/.
136 - Sabine Harribey 2021
We compute the four-loop beta functions of short and long-range multi scalar models with general sextic interactions and complex fields. We then specialize the beta functions to a $U(N)^3$ symmetry and study the renormalization group at next-to-leadi ng order in $N$ and small $epsilon$. In the short-range case, $epsilon$ is the deviation from the critical dimension while it is the deviation from the critical scaling of the free propagator in the long-range case. This allows us to find the $1/N$ corrections to the rank-3 sextic tensor model of arXiv:1912.06641. In the short-range case, we still find a non-trivial real IR stable fixed point, with a diagonalizable stability matrix. All couplings, except for the so-called wheel coupling, have terms of order $epsilon^0$ at leading and next-to-leading order, which makes this fixed point different from the other melonic fixed points found in quartic models. In the long-range case, the corrections to the fixed point are instead not perturbative in $epsilon$ and hence unreliable; we thus find no precursor of the large-$N$ fixed point.
We study the bootstrap method in harmonic oscillators in one-dimensional quantum mechanics. We find that the problem reduces to the Diracs ladder operator problem and is exactly solvable. Thus, harmonic oscillators allow us to see how the bootstrap method works explicitly.
193 - Cao H. Nam 2021
Studying the color superconductivity (CSC) phase is important to understand the physics in the core of the neutron stars which is the only known context where the gravitational force squeezes the matter to the sufficiently high density and hence the CSC phase might appear. We propose a simple holographic dual description of the CSC phase transition in the realistic Yang-Mills theory with a power-law Maxwell field. We find the CSC phase transition with the large color number in the deconfinement phase, which is not found in the case of the usual Maxwell field, if the power parameter characterizing for the power-law Maxwell field is sufficiently lower than one but above $1/2$ and the chemical potential is above a critical value. However, the power parameter is not arbitrary below one because when this parameter is sufficiently far away from one it leads to the occurrence of the CSC state in the confinement phase which is not compatible with a nonzero vacuum expectation value of the color nonsinglet operator.
A characteristic value formulation of the Weyl double copy leads to an asymptotic formulation. We find that the Weyl double copy holds asymptotically in cases where the full solution is algebraically general, using rotating STU supergravity black hol es as an example. The asymptotic formulation provides clues regarding the relation between asymptotic symmetries that follows from the double copy. Using the C-metric as an example, we show that a previous interpretation of this gravity solution as a superrotation has a single copy analogue relating the appropriate Lienard-Wiechert potential to a large gauge transformation.
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