High Energy Physics Theory

We examine various properties of double field theory and the doubled string sigma model in the context of geometric quantisation. In particular we look at T-duality as the symplectic transformation related to an alternative choice of polarisation in the construction of the quantum bundle for the string. Following this perspective we adopt a variety of techniques from geometric quantisation to study the doubled space. One application is the construction of the double coherent state that provides the shortest distance in any duality frame and a stringy deformed Fourier transform.

We consider a short rollercoaster cosmology based on two stages of monodromy inflation separated by a stage of matter domination, generated after the early inflaton falls out of slow roll. If the first stage is controlled by a flat potential,V???pwithp<1and lastsN??0??0efolds, the scalar and tensor perturbations at the largest scales will fit the CMB perfectly, and produce relic gravity waves with0.02?�r??.06, which can be tested by LiteBIRD and CMB-S4 experiments. If in addition the first inflaton is strongly coupled to a hidden sectorU(1), there will be an enhanced production of vector fluctuations near the end of the first stage of inflation. These modes convert rapidly to tensors during the short epoch of matter domination, and then get pushed to superhorizon scales by the second stage of inflation, lasting another20??0efolds. This band of gravity waves is chiral, arrives today with wavelengths in the range of108km, and with amplitudes greatly enhanced compared to the long wavelength CMB modes by vector sources. It is therefore accessible to LISA. Thus our model presents a rare early universe theory predicting several simultaneous signals testable by a broad range of gravity wave searches in the very near future.

In this paper we study the dynamics of explicit solutions of2+1-dimensional (2D) sine-Gordon equation. The Darboux transformation is applied to the associated linear eigenvalue problem to construct nontrivial solutions of2D sine-Gordon equation in terms of ratios of determinants. We obtained a generalized expression forN-fold transformed dynamical variable which enables us to calculate explicit expressions of nontrivial solutions. In order to explore the dynamics of kink soliton solutions explicit expressions one- and two-soliton solutions are derived for particular column solutions. Different profiles of kink-kink and, kink and anti-kink interactions are illustrated for a different parameters and arbitrary functions. First-order bound state solution is also displayed in our work.

We study the quantum evolution of the early universe, its semi-classical analogue together with inflationary regime, in view of a generalized modified theory of gravity. The action is built by supplementing the non-minimally coupled scalar-tensor theory of gravity with scalar curvature squared term and a Gauss-Bonnet-dilatonic coupled term. It is generalized, since all the parameters are treated as arbitrary functions of the scalar field. It is interesting to explore the fact that instead of considering additional flow parameters, an effective potential serves the purpose of finding inflationary parameters. The dilaton stabilization issue appears here as a problem with reheating. Addition of a cosmological constant term alleviates the problem, and inflation is effectively driven by the vacuum energy density. Thus Gauss-Bonnet term might play a significant role in describing late-time cosmic evolution.

An effective theory for 2D non-Abelian topological BF theory is investigated. We develop a systematic approach by integrating out the non-Abelian gauge fields to obtain an effective theory containing solely scalar fields. Expressions for the SU(2) and SU(3) effective actions are explicitly stated. In the case of SU(2), we show that the effective action can be interpreted as a winding number. By using the SU(2) effective action, the partition function on a sphere for SU(2) Yang-Mills theory is calculated. Moreover, we generalise the theory to include a source term for the gauge field as well as calculate the vacuum expectation value of the Wilson loop based on the effective theory. The result obeys the area law agreeing with known results.

We discuss interacting, closed, bosonic and superstrings in thermal equilibrium at temperatures close to the Hagedorn temperature in flat space. We calculate S-matrix elements of the strings at the Hagedorn temperature and use them to construct a low-energy effective action for interacting strings near the Hagedorn temperature. We show, in particular, that the four-point amplitude of massless winding modes leads to a positive quartic interaction. Furthermore, the effective field theory has a generalized conformal structure, namely, it is conformally invariant when the temperature is assigned an appropriate scaling dimension. Then, we show that the equations of motion resulting from the effective action possess a winding-mode-condensate background solution above the Hagedorn temperature and present a worldsheet conformal field theory, similar to a Sine-Gordon theory, that corresponds to this solution. We find that the Hagedorn phase transition in our setup is second order, in contrast to a first-order transition that was found previously in different setups.

We find all analytic SU(2) Yang-Mills solutions on de Sitter space by reducing the field equations to Newton's equation for a particle in a particular 3d potential and solving the latter in a special case. In contrast, Maxwell's equations on de Sitter space can be solved in generality, by separating them in hysperspherical coordinates. Employing a well-known conformal map between (half of) de Sitter space and (the future half of) Minkowski space, the Maxwell solutions are mapped to a complete basis of rational electromagnetic knot configurations. We discuss some of their properties and illustrate the construction method with two nontrivial examples given by rational functions of increasing complexity. The material is partly based on [1,2].

We present an exact computation of effective Hamiltonians for an elementary model obtained from the Yukawa theory by going to the limit of bare fermions being infinitely heavy and bare bosons being at rest with respect to the fermions that emit or absorb them. The coupling constant can be arbitrarily large. The Hamiltonians are computed by solving the differential equation of the renormalization group procedure for effective particles (RGPEP). Physical fermions, defined in the model as eigenstates of the effective Hamiltonians, are obtained in the form of an effective fermion dressed with a coherent state of effective bosons. The model computation illustrates the method that can be used in perturbative computations of effective Hamiltonians for realistic theories. It shows the mechanism by which the perturbative expansion and Tamm-Dancoff approximation increase in accuracy along the RGPEP evolution.

In this paper we describe a systematic method to compute elliptic genera of (2,2) supersymmetric gauge theories in two dimensions with gauge group G/Gamma (for G semisimple and simply-connected, Gamma a subgroup of the center of G) with various discrete theta angles. We apply the technique to examples of pure gauge theories with low-rank gauge groups. Our results are consistent with expectations from decomposition of two-dimensional theories with finite global one-form symmetries and with computations of supersymmetry breaking for some discrete theta angles in pure gauge theories. Finally, we make predictions for the elliptic genera of all the other remaining pure gauge theories by applying decomposition and matching to known supersymmetry breaking patterns.

We take the tensor network describing explicit p-adic CFT partition functions proposed in [1], and considered boundary conditions of the network describing a deformed Bruhat-Tits (BT) tree geometry. We demonstrate that this geometry satisfies an emergent graph Einstein equation in a unique way that is consistent with the bulk effective matter action encoding the same correlation function as the tensor network, at least in the perturbative limit order by order away from the pure BT tree. Moreover, the (perturbative) definition of the graph curvature in the Mathematics literature naturally emerges from the consistency requirements of the emergent Einstein equation. This could provide new insights into the understanding of gravitational dynamics potentially encoded in more general tensor networks.