String Gas Research Articles

Gravitational index of the heterotic string

The fundamental heterotic string has a tower of BPS states whose supersymmetric index has an exponential growth in the charges. We construct the saddle-point of the gravitational path integral corresponding to this index. The saddle-point configuration is a supersymmetric rotating non-extremal Euclidean black hole. This configuration is singular in the two-derivative theory. We show that the addition of higher-derivative terms in four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supergravity resolves the singularity. In doing so, we extend the recently-developed “new attractor mechanism” to include the effect of higher-derivative terms. Remarkably, the one-loop, four-derivative F-term contribution to the prepotential leads to a precise match of the gravitational and microscopic index. We also comment, using the effective theory near the horizon, on the possibility of a string-size near-extremal black hole. Our results clarify the meaning of different descriptions of this system in the literature. The thermal state transitions to a winding condensate and a gas of strings without ever reaching a small black hole, while the index is captured by the rotating Euclidean black hole solution and is constant and thus smoothly connected to the microscopic ensemble.

Superstring cosmology — a complementary review

In this review, a number of approaches to superstring cosmology which make use of key features which distinguish string theory from point particle theories are discussed, with particular emphasis on emergent scenarios. One motivation for the discussion is the realization that, in order to describe the evolution of the very early universe, it is necessary to go beyond a conventional effective field theory (EFT) analysis. Some of the conceptual problems of an EFT analysis will be discussed. The review begins with a summary of the criteria for a successful early universe scenario, emphasizing that cosmic inflation is not the only scenario of early universe cosmology which is consistent with current cosmological observations. Bouncing and emergent scenarios as interesting alternatives are introduced. Some realizations of these scenarios from superstring theory are reviewed, e.g. String Gas Cosmology, the Pre-Big-Bang scenario, the Ekpyrotic model, Double Field Theory cosmology and matrix model cosmology. In light of the difficulties in obtaining cosmic inflation from string theory (at the level of EFT), and realizing that there are promising examples of alternative early universe scenarios which are derived from basic principles of superstring theory, one must entertain the possibility that the cosmology emerging from string theory will not involve an extended period of accelerated expansion.

Features of gravitational interaction as the basis of “Dark Energy” in the gas of null strings

In this work, the influence of the shape of the null strings that form the gas on the gravitational properties and evolution of the null string gas was investigated. An interesting result of the study is that the test null string, being in the interaction zone, can only have a shape that exactly repeats the shape of the source string. As a result, null strings having different spatial forms can be located in the gas only outside the zone of interaction with each other. The “size” (width) of the zone of interaction of each null string in the gas is determined by the value of its initial momenta, and for some critical values it can occupy the entire space. The size (width) and “impenetrability” of the interaction zones for null strings having different spatial shapes can be a physical source of “strong” gravitational repulsion in the gas of null strings. In turn, the “strong” gravitational repulsion between null strings with different spatial shapes can be a source of a long-term accelerated expansion of such a gas (a source of “dark energy”).

Spectral form factor for free large N gauge theory and strings

We investigate the spectral form factor in two different systems, free large N gauge theories and highly excited string gas. In both cases, after a rapid decay of the spectral form factor at early time, new contributions come in, preventing the spectral form factor from ever becoming exponentially small. We consider U(N) gauge theories with only adjoint matter and compute the spectral form factor using a matrix integral of the thermal holonomy U. The new saddles differ from the early time saddle by preserving certain subgroups of the center symmetry. For a gas of strings, the short time decay of the spectral form factor is governed by the continuous Hagedorn density of states, which can be associated to the thermal winding mode with winding number ±1. We show that the rise of the spectral form factor comes from other winding modes that also carry momentum along the time direction. We speculate on the existence of a family of classical solutions for these string modes, similar to the Horowitz-Polchinski solution.We review a similar problem for black holes. In particular, we examine the Kontsevich-Segal criterion on complex black holes that contribute to the spectral form factor. In the canonical ensemble quantity Z(β + it), the black hole becomes unallowed at t ~ mathcal{O} (β). A way to avoid this is to consider the microcanonical ensemble, where the black hole stays allowable.

Anisotropic Conformal Model in $f(R, \phi)$ Theory

In this study, we examine conformal spherically symmetric spacetime with anisotropic fluid in $f(R,ϕ)$ theory. The exact solutions of field equations are obtained for $f(R,ϕ)=(1+λη^2 ϕ^2 )R$ model. All the quantities for anisotropic fluid are investigated through equation of state constant, $ω$. The models for three different selections of $ω$ are represented for the constructed model. Moreover, string gas is the only condition that anisotropic fluid behaves as an isotropic fluid for the constructed model. Furthermore, the anisotropy parameter and causality conditions are examined. Lastly, the results for the solutions are concluded from the physical and geometrical viewpoint.

Asymptotically free AdS3/CFT2

We propose a new AdS3/CFT2 duality, in which the bulk string theory has a target spacetime AdS3 times a squashed three-sphere {mathbbm{S}}_{flat}^3 , and the dual CFT2 is a symmetric product of sigma models on ℝϕ× {mathbbm{S}}_{flat}^3 , deformed by a ϕ-dependent ℤ2 twist operator. The duality maps the asymptotic region of AdS3 to the region ϕ → ∞, where the twist interaction in the CFT2 turns off. The AdS3 backgrounds in question have RAdS< ℓs, and so lie on the string side of the string/black hole correspondence transition. As a consequence, the high energy density of states consists of a string gas in AdS3 rather than an ensemble of BTZ black holes. This property allows us to derive the dual CFT2 by a systematic analysis of the worldsheet string theory on AdS3.

Comparative Analysis of Standard ΛCDM and ΛCS Models

We draw a comparison of time-dependent cosmological parameters calculated in the standard ΛCDM model with those of the model of a homogeneous and isotropic Universe with non-zero cosmological constant filled with a perfect gas of low-velocity cosmic strings (ΛCS model). It is shown that pressure-free matter can obtain the properties of a gas of low-velocity cosmic strings in the epoch, when the global geometry and the total amount of matter in the Universe as a whole obey an additional constraint. This constraint follows from the quantum geometrodynamical approach in the semiclassical approximation. In terms of general relativity, its effective contribution to the field equations can be linked to the time evolution of the equation of state of matter caused by the processes of redistribution of the energy between matter components. In the present article, the exact solutions of the Einstein equations for the ΛCS model are found. It is demonstrated that this model is equivalent to the open de Sitter model. After the scale transformation of the time variable of the ΛCS model, the standard ΛCDM and ΛCS models provide the equivalent descriptions of cosmological parameters as functions of time at equal values of the cosmological constant. The exception is the behavior of the deceleration parameter in the early Universe.

Improved DHOST Genesis

We improve the DHOST Genesis proposed in [1], such that the near scale invariant scalar power spectrum can be generated from the model itself, without invoking extra mechanism like a string gas. Besides, the superluminality problem of scalar perturbation plagued in [1] can be rescued by choosing proper DHOST action.

Detecting transition between Abelian and non-Abelian topological orders through symmetric tensor networks

We propose a unified scheme to identify phase transitions out of the $\mathbb{Z}_2$ Abelian topological order, including the transition to a non-Abelian chiral spin liquid. Using loop gas and and string gas states [H.-Y. Lee, R. Kaneko, T. Okubo, N. Kawashima, Phys. Rev. Lett. 123, 087203 (2019)] on the star lattice Kitaev model as an example, we compute the overlap of minimally entangled states through transfer matrices. We demonstrate that, similar to the anyon condensation, continuous deformation of a $\mathbb{Z}_2$-injective projected entangled-pair state (PEPS) also allows us to study the transition between Abelian and non-Abelian topological orders. We show that the charge and flux anyons defined in the Abelian phase transmute into the $\sigma$ anyon in the non-Abelian topological order. Furthermore, we show that contrary to the claim in [Phys. Rev. B 101, 035140 (2020)], both the LG and SG states have infinite correlation length in the non-Abelian regime, consistent with the no-go theorem that a chiral PEPS has a gapless parent Hamiltonian.

Note on shape moduli stabilization, string gas cosmology and the swampland criteria

In String Gas Cosmology, the simplest shape modulus fields are naturally stabilized by taking into account the presence of string winding and momentum modes. We determine the resulting effective potential for these fields and show that it obeys the de Sitter conjecture, one of the swampland criteria for effective field theories to be consistent with superstring theory.

Mass Generation by a Massless Scalar Field

We propose a possibility of qualitatively taking into account the mutual influence of two gravitationally interacting null strings (thin tubes of a massless scalar field) on the motion of each of them. It is shown that it is possible to implement a self-consistent motion of two null strings in which their mutual gravitational influence leads to vibrations of each string inside a bounded spatial region. Such systems of gravitationally interacting null strings can be considered as primary particles in a null string gas with a nonzero rest mass. Gravitationally interacting primary particles can combine into more complex formations, “macro” objects. A peculiar feature of such “macro” formations in the null string gas is the fundamental impossibility of having a completely formed structure (in the null string gas, there are inevitable processes leading to a random (dynamic) change in the number of null strings that gravitationally belong to the “macro” object). By averaging various spatial distributions of “macro” formations over time, it is possible to introduce the concepts of “substance” and “interaction fields” in the null string gas.

Gravitational Interaction in a Null String Gas and Its Possible Consequences

In this paper, we investigated the possible consequences of gravitational interaction in a gas of null strings. The structural elements of this gas are closed null strings in the form of a circle (thin closed tubes of massless scalar field). A possibility to qualitatively take into account the mutual influence on motion for gravitationally interacting null strings is proposed. It is shown that the result of gravitational interaction is the self-consistent motion of two null strings inside a space-limited region. Such systems of gravitationally interacting null strings can be considered as primary particles in a gas of null strings with an effective nonzero rest mass. It is noted that the “lifetime” of such particles should depend on external conditions. Long-term existence (“lifetime”) of primary particles is possible if they are combined into more complex structures. The possibility of such a union depends on the motion direction of the null strings forming the particles. The most interesting is the possibility of combining primary particles into spherically symmetric formations—“macro” objects. A feature of such “macro” formations in a gas of null strings is the fundamental impossibility to have finally formed structure. In a gas of null strings, processes leading to a random (dynamic) change in the number of null strings gravitationally belonging to a “macro” object are inevitable. By averaging over time the various spatial distributions of the “macro” formations, the concepts of “substance” and “interaction field” can be introduced in a gas of null strings.

Unstable D-brane in torsional Newton-Cartan background

This paper is devoted to the construction of unstable D-brane action in torsional Newton-Cartan background through T-duality along null direction. We determine corresponding equations of motion and analyze their solution that corresponds to lower dimensional non-relativistic D(p-1)-brane. We also find Hamiltonian for unstable Dp-brane and study tachyon vacuum solutions that can be interpreted as gas of non-relativistic strings.

String gases and the swampland

In this paper, we study some aspects of moduli stabilization using string gases in the context of the Swampland. In the framework which we derive, the matter Lagrangian for string gases yields a potential for the size moduli which satisfies the de Sitter conjecture with the condition |∇ V|/V ⩾ 1/√p 1/Mp, where p is the number of compactified dimensions. Moreover, the moduli find themselves stabilized at the self-dual radius, and gravity naturally emerges as the weakest force.

Strings, symmetric products, [formula omitted] deformations and Hecke operators

We derive a formula for the torus partition sum of the symmetric product of TT¯ deformed CFT's, using previous work on long strings in (deformed) AdS3, and universality. The result is given by an integral transform of the partition function for the block of the symmetric product, summed over its Hecke transforms, and is manifestly modular invariant. The spectrum is interpretable as a gas of multiply wound long strings with a particular orientation.

Creating spatial flatness by combining string gas cosmology and power law inflation

We show that it is possible to combine an early phase of String Gas Cosmology which can explain the origin of the observed structures on cosmological scales with a short later period of power law inflation which creates spatial flatness. The resulting model is consistent with the ``swampland criteria'' and the constraints coming from the {\it Trans-Planckian Censorship Conjecture}. Such a construction is not possible using only canonical slow-roll inflation, but it can emerge in the warm inflation scenario or in cold inflation with an exponential potential. The resulting cosmology is non-singular. We discuss the spectrum of cosmological perturbations resulting in our scenario. On large scales (scales which remain larger than the Hubble radius after the initial string gas phase) the spectrum is determined by the thermal string gas fluctuations set up in the primordial phase, and it is almost scale-invariant with a slight red tilt. On small scales, the perturbations produced during the inflationary phase dominate. On these scales, the spectrum is once again nearly scale-invariant. There is an intermediate range (scales which enter the Hubble radius during the period of inflation) where the string gas fluctuations are damped but continue to dominate over those produced during the period of inflation. On these scales the spectrum has a sharp red spectral index of $n_s - 1 \sim -2$.

Nonsingular ekpyrotic cosmology with a nearly scale-invariant spectrum of cosmological perturbations and gravitational waves

We propose a mechanism borrowed from string theory which yields a nonsingular transition from a phase of ekpyrotic contraction to the expanding phase of standard big bang cosmology. The same mechanism converts the initial vacuum spectrum of cosmological fluctuations before the bounce into a scale-invariant one, and also changes the spectrum of gravitational waves into an almost scale-invariant one. The scalar and tensor tilts are predicted to be the same, in contrast to the predictions from the ``string gas cosmology'' scenario. The amplitude of the gravitational wave spectrum depends on the ratio of the string scale to the Planck scale and may be in reach of upcoming experiments.

Abelian and non-Abelian chiral spin liquids in a compact tensor network representation

We provide new insights into the Abelian and non-Abelian chiral Kitaev spin liquids on the star lattice using the recently proposed loop gas (LG) and string gas (SG) states [H.-Y. Lee, R. Kaneko, T. Okubo, N. Kawashima, Phys. Rev. Lett. 123, 087203 (2019)]. Those are compactly represented in the language of tensor network. By optimizing only one or two variational parameters, accurate ansatze are found in the whole phase diagram of the Kitaev model on the star lattice. In particular, the variational energy of the LG state becomes exact(within machine precision) at two limits in the model, and the criticality at one of those is analytically derived from the LG feature. It reveals that the Abelian CSLs are well demonstrated by the short-ranged LG while the non-Abelian CSLs are adiabatically connected to the critical LG where the macroscopic loops appear. Furthermore, by constructing the minimally entangled states and exploiting their entanglement spectrum and entropy, we identify the nature of anyons and the chiral edge modes in the non-Abelian phase with the Ising conformal field theory.

Solution of Einstein’s Equations for a Closed Null String with Axial Symmetry that Is Radially Increasing Its Size

A solution to the Einstein equations for a closed null string with axial symmetry that is radially increases its size is found. The possibility of choosing the ideal gas of null strings as a dominant source of gravity is confirmed in the study of the null string inflation mechanism in Friedmann–Robertson–Walker spaces. The absence of a limit transition between the solution that is found and the solution for a closed circular null string that is radially changing its size is shown. This indicates the stability of the configuration of a closed circular null string during its motion in an external gravitational field. It is noted that part of the characteristics of the null string gas, such as the ability to form a domain structure and existence of stable polarized states (multi-string systems), are independent of the shape of null string, but the dynamics of the test null string in a field of such multi-string system has singularities.

Some physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology

The way physics of loop quantum gravity is affected by the underlying quantization ambiguities is an open question. We address this issue in the context of loop quantum cosmology using gauge-covariant fluxes. Consequences are explored for two choices of regularization parameters: ${\ensuremath{\mu}}_{0}$ and $\overline{\ensuremath{\mu}}$ in the presence of a positive cosmological constant, and two choices of regularizations of the Hamiltonian constraint in loop quantum cosmology: the standard and the Thiemann regularization. We show that novel features of singularity resolution and bounce, occurring due to gauge-covariant fluxes, exist also for Thiemann-regularized dynamics. The ${\ensuremath{\mu}}_{0}$ scheme is found to be unviable as in standard loop quantum cosmology when a positive cosmological constant is included. Our investigation brings out a surprising result that the nature of emergent matter in the prebounce regime is determined by the choice of regulator in the Thiemann regularization of the scalar constraint whether or not one uses gauge-covaraint fluxes. Unlike the $\overline{\ensuremath{\mu}}$ scheme where the emergent matter is a cosmological constant, the emergent matter in the ${\ensuremath{\mu}}_{0}$ scheme behaves as a string gas.