arXiv subjects

Yuho Sakatani

Publications and source records attributed to Yuho Sakatani.

45 records · Page 3Linked to original sources

arXiv2015

$\mathbf{O}(D,D)$ Covariant Noether Currents and Global Charges in Double Field Theory

Double field theory is an approach for massless modes of string theory, unifying and geometrizing all gauge invariance in manifest $\mathbf{O}(D,D)$ covariant manner. In this approach, we derive off-shell conserved Noether current and corresponding Noether potential associated with unified gauge invariance. We add Wald-type counter two-form to the Noether potential and define conserved global charges as surface integral. We check our $\mathbf{O}(D,D)$ covariant formula against various string backgrounds, both geometric and non-geometric. In all cases we examined, we find perfect agreements with previous results. Our formula facilitates to evaluate momenta along not only ordinary spacetime directions but also dual spacetime directions on equal footing. From this, we confirm recent assertion that null wave in doubled spacetime is the same as macroscopic fundamental string in ordinary spacetime.

hep-th↗

arXiv2015

Defect branes as Alice strings

There exist various defect-brane backgrounds in supergravity theories which arise as the low energy limit of string theories. These backgrounds typically have non-trivial monodromies, and if we move a charged probe around the center of a defect, its charge will be changed by the action of the monodromy. During the process, the charge conservation law seems to be violated. In this paper, to resolve this puzzle, we examine a dynamics of the charge changing process and show that the missing charge of the probe is transferred to the background. We then explicitly construct the resultant background after the charge transfer process by utilizing dualities. This background has the same monodromy as the original defect brane, but has an additional charge which does not have any localized source. In the literature, such a charge without localized source is known to appear in the presence of Alice strings. We argue that defect branes can in fact be regarded as a realization of Alice strings in string theory and examine the charge transfer process from that perspective.

hep-th↗

arXiv2015

Exotic branes and non-geometric fluxes

We present and study ten-dimensional effective actions for various non-geometric fluxes of which exotic branes act as the magnetic sources. Each theory can be regarded as a U-dual version of the $β$-supergravity, a reformulation of the ten-dimensional supergravity which is suitable for describing non-geometric backgrounds with Q-flux. In each theory, we find a solution that corresponds to the background of an exotic brane and show that it is single-valued up to a gauge transformation, although the same background written in the standard background fields is not single-valued in a usual sense. Further, we also find a solution which corresponds to the background of an instanton that is the electric dual of the exotic brane and discuss its properties.

hep-th↗

arXiv2014

Master equation for the Unruh-DeWitt detector and the universal relaxation time in de Sitter space

We derive the master equation that completely determines the time evolution of the density matrix of the Unruh-DeWitt detector in an arbitrary background geometry. We apply the equation to reveal a nonequilibrium thermodynamic character of de Sitter space. This generalizes an earlier study on the thermodynamic property of the Bunch-Davies vacuum that an Unruh-DeWitt detector staying in the Poincare patch and interacting with a scalar field in the Bunch-Davies vacuum behaves as if it is in a thermal bath of finite temperature. In this paper, instead of the Bunch-Davies vacuum, we consider a class of initial states of scalar field, for which the detector behaves as if it is in a medium that is not in thermodynamic equilibrium and that undergoes a relaxation to the equilibrium corresponding to the Bunch-Davies vacuum. We give a prescription for calculating the relaxation times of the nonequilibrium processes. We particularly show that, when the initial state of the scalar field is the instantaneous ground state at a finite past, the relaxation time is always given by a universal value of half the curvature radius of de Sitter space. We expect that the relaxation time gives a nonequilibrium thermodynamic quantity intrinsic to de Sitter space.

hep-th↗

arXiv2013

Propagators in de Sitter space

In a spacetime with no global timelike Killing vector, we do not have a natural choice for the vacuum state of matter fields, leading to an ambiguity in defining the Feynman propagators. In this paper, taking the vacuum state to be the instantaneous ground state of the Hamiltonian at each moment, we develop a method for calculating wave functions associated with the vacuum and the corresponding in-in and in-out propagators. We apply this method to free scalar field theory in de Sitter space and obtain de Sitter invariant propagators in various coordinate patches. We show that the in-out propagator in the Poincare patch has a finite massless limit in a de Sitter invariant form. We argue and numerically check that our in-out propagators agree with those obtained by a path integral with the standard iεprescription, and identify the condition on a foliation of spacetime under which such coincidence can happen for the foliation. We also show that the in-out propagators satisfy Polyakov's composition law. Several applications of our framework are also discussed.

hep-th↗

arXiv2012

Rotating string in doubled geometry with generalized isometries

In this paper, we first construct a globally well-defined non-geometric background which contains several branes in type II string theory compactified on a 7-torus. One of these branes is called 5^2_2, which is a codimension-2 object and has a non-trivial monodromy given by a T-duality transformation. The geometry near the 5^2_2-brane is shown to approach the non-geometric background constructed in arXiv:1004.2521. We then construct the solution of a fundamental string rotating along a non-trivial cycle in the 5^2_2 background. Although the background is not axisymmetric in the usual sense, we show that it is actually axisymmetric as a doubled geometry by explicitly finding a generalized Killing vector. We perform a generalized coordinate transformation into a system where the generalized isometry is manifest, and show that the winding and momentum charges of the string solution is explicitly conserved in that system.

hep-th↗

arXiv2012

Conformal higher-order viscoelastic fluid mechanics

We present a generally covariant formulation of conformal higher-order viscoelastic fluid mechanics with strain allowed to take arbitrarily large values. We give a general prescription to determine the dynamics of a relativistic viscoelastic fluid in a way consistent with the hypothesis of local thermodynamic equilibrium and the second law of thermodynamics. We then elaborately study the transient time scales at which the strain almost relaxes and becomes proportional to the gradients of velocity. We particularly show that a conformal second-order fluid with all possible parameters in the constitutive equations can be obtained without breaking the hypothesis of local thermodynamic equilibrium, if the conformal fluid is defined as the long time limit of a conformal second-order viscoelastic system. We also discuss how local thermodynamic equilibrium could be understood in the context of the fluid/gravity correspondence.

hep-th↗

arXiv2011

Entropic formulation of relativistic continuum mechanics

An entropic formulation of relativistic continuum mechanics is developed in the Landau-Lifshitz frame. We introduce two spatial scales, one being the small scale representing the linear size of each material particle and the other the large scale representing the linear size of a large system which consists of the material particles and is to linearly regress to the equilibrium. We propose a local functional which is expected to represent the total entropy of the larger system and require the entropy functional to be maximized in the process of linear regression. We show that Onsager's original idea on linear regression can then be realized explicitly as current conservations with dissipative currents in the desired form. We demonstrate the effectiveness of this formulation by showing that one can treat a wide class of relativistic continuum materials, including standard relativistic viscous fluids and relativistic viscoelastic materials.

hep-th↗

arXiv2011

Relativistic viscoelastic fluid mechanics

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski spacetime become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

cond-mat.stat-mech↗