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Register a new userDynamics of Perturbations in Double Field Theory & Non-Relativistic String Theory
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Double Field Theory provides a geometric framework capable of describing string theory backgrounds that cannot be understood purely in terms of Riemannian geometry -- not only globally (`non-geometry), but even locally (`non-Riemannian). In this work, we show that the non-relativistic closed string theory of Gomis and Ooguri [1] arises precisely as such a non-Riemannian string background, and that the Gomis-Ooguri sigma model is equivalent to the Double Field Theory sigma model of [2] on this background. We further show that the target-space formulation of Double Field Theory on this non-Riemannian background correctly reproduces the appropriate sector of the Gomis-Ooguri string spectrum. To do this, we develop a general semi-covariant formalism describing perturbations in Double Field Theory. We derive compact expressions for the linearized equations of motion around a generic on-shell background, and construct the corresponding fluctuation Lagrangian in terms of novel completely covariant second order differential operators. We also present a new non-Riemannian solution featuring Schrodinger conformal symmetry.
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In this paper, we analyze the inflationary cosmology using string field theory. This is done by using the zero level contribution from string field theory, which is a non-local tachyonic action. We will use the non-local Friedmann equations for this model based on string field theory, and calculate the slow-roll parameters for this model. We will then explicitly obtain the scalar and tensorial power spectrum, their related indices, and the tensor-to-scalar ratio for this model. Finally, we use cosmological data from Planck 2013 to 2018 to constrain the free parameters in this model and find that string field theory is compatible with them.
Taking $mathbf{O}(D,D)$ covariant field variables as its truly fundamental constituents, Double Field Theory can accommodate not only conventional supergravity but also non-Riemannian gravities that may be classified by two non-negative integers, $(n,bar{n})$. Such non-Riemannian backgrounds render a propagating string chiral and anti-chiral over $n$ and $bar{n}$ dimensions respectively. Examples include, but are not limited to, Newton--Cartan, Carroll, or Gomis--Ooguri. Here we analyze the variational principle with care for a generic $(n,bar{n})$ non-Riemannian sector. We recognize a nontrivial subtlety for ${nbar{n} eq 0}$ that infinitesimal variations generically include those which change $(n,bar{n})$. This seems to suggest that the various non-Riemannian gravities should better be identified as different solution sectors of Double Field Theory rather than viewed as independent theories. Separate verification of our results as string worldsheet beta-functions may enlarge the scope of the string landscape far beyond Riemann.
We investigate a class of exactly solvable quantum quench protocols with a finite quench rate in systems of one dimensional non-relativistic fermions in external harmonic oscillator or inverted harmonic oscillator potentials, with time dependent masses and frequencies. These hamiltonians arise, respectively, in harmonic traps, and the $c=1$ Matrix Model description of two dimensional string theory with time dependent string coupling. We show how the dynamics is determined by a single function of time which satisfies a generalized Ermakov-Pinney equation. The quench protocols we consider asymptote to constant masses and frequencies at early times, and cross or approach a gapless potential. In a right side up harmonic oscillator potential we determine the scaling behavior of the one point function and the entanglement entropy of a subregion by obtaining analytic approximations to the exact answers. The results are consistent with Kibble-Zurek scaling for slow quenches and with perturbation calculations for fast quenches. For cis-critical quench protocols the entanglement entropy oscillates at late times around its initial value. For end-critical protocols the entanglement entropy monotonically goes to zero inversely with time, reflecting the spread of fermions over the entire line. For the inverted harmonic oscillator potential, the dual collective field description is a scalar field in a time dependent metric and dilaton background.
We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N=4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and non-conformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.
We present a new supersymmetric, asymptotically flat, black hole solution to five-dimensional U(1)^3-supergravity which is regular on and outside an event horizon of lens space topology L(2,1). The solution has seven independent parameters and uplifts to a family of 1/8-supersymmetric D1-D5-P black brane solutions to Type IIB supergravity. The decoupling limit is asymptotically AdS(3) x S^3 x T^4, with a near-horizon geometry that is a twisted product of the near-horizon geometry of the extremal BTZ black hole and L(2,1) x T^4, although it is not (locally) a product space in the bulk. We show that the decoupling limit of a special case of the black lens is related to that of a black ring by spectral flow, thereby supplying an account of its entropy. Analogous solutions of U(1)^N-supergravity are also presented.
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