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Construction of a universal finite-type invariant can be reduced, under suitable assumptions, to the solution of certain equations (the hexagon and pentagon equations) in a particular graded associative algebra of chord diagrams. An…
A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations $|Ax|^2=y$. The algorithms are developed by exploiting the inherent low rank structure of the problem based on the…
The spacetime physics of bulk closed string tachyon condensation is studied at the level of a two-derivative effective action. We derive the unique perturbative tachyon potential consistent with a full class of linearized tachyonic…
Using analytical methods, a nonpertubative vacuum is constructed recursively in the field theory for the open bosonic string. Evidence suggests it corresponds to the Lorentz-invariant endpoint of tachyon condensation on a D25-brane. The…
Motivated by recent discussions of actions for tachyon and vector fields related to tachyon condensation in open string theory we review and clarify some aspects of their derivation within sigma model approach. In particular, we demonstrate…
We analyze the consistency of a recently proposed real tachyon vacuum solution without square roots in open bosonic string field theory. We show that the equation of motion contracted with the solution itself is satisfied. Additionally, by…
We consider bosonic open string field theory in marginally deformed backgrounds, which is obtained by expanding the string field around the identity-based solutions associated with marginal deformations. We find a new set of string fields…
An exact solution to the vacuum Einstein equations is presented, whose structure is based on the Hopf fibration. The solution employs a geodesic null vector field that defines a twisting congruence and appears in the metric in Kerr-Schild…
We derive an analytic series solution of the elliptic equations providing the 4-tachyon off-shell amplitude in cubic string field theory (CSFT). From such a solution we compute the exact coefficient of the quartic effective action relevant…
We study formal expansions of asymptotically flat solutions to the static vacuum field equations which are determined by minimal sets of freely specifyable data referred to as `null data'. These are given by sequences of symmetric trace…
We investigate static cylindrically symmetric vacuum solutions in Weyl coordinates in the framework of f(T) theories of gravity, where T is the torsion scalar. The set of modified Einstein equations is presented and the fourth coming…
We explore the vacuum structure in bosonic open string field theory expanded around an identity-based solution parameterized by $a(>=-1/2)$. Analyzing the expanded theory using level truncation approximation up to level 20, we find that the…
Motivated by the algebraic open-closed string models, we introduce and discuss an infinite-dimensional counterpart of the open-closed Hurwitz theory describing branching coverings generated both by the compact oriented surfaces and by the…
Cosmological implication of rolling tachyons is reported in the context of effective field theory. With a brief review of rolling tachyons in both flat and curved spacetimes, we study the string cosmological model with both tachyon and…
We consider the backreaction problem of a quantized minimally coupled massless scalar field in cosmology. The adiabatically regularized stress-energy tensor in a general Friedmann-Robertson-Walker background is approximately evaluated by…
We derive the $\sigma$-model tachyon $\beta$-function equation of 2-dimensional string theory, in the background of flat space and linear dilaton, working entirely within the $c=1$ matrix model. The tachyon $\beta$-function equation is…
We investigate the tachyon coupling in a static Robertson--Walker like metric background. For a tachyon and dilaton field which are only time dependent one can rewrite this model as a SU(2) Wess--Zumino--Witten model and a scalar…
We argue that the Leutheusser-Liu procedure of isolating a von Neumann algebra in the $N = \infty$ limit of string theories, leads to the algebra of relativistic fermion fields on a half line for the $c = 1$ string theory. This is a Type…
We demonstrate that, upon minimizing a renormalizable, single-scalar potential invariant under a non-Abelian symmetry, special orientations in the associated vacuum alignment of the scalar multiplet correspond to the preservation of a…
Strong field (exact) solutions of the gravitational field equations of General Relativity in the presence of a Cosmological Constant are investigated. In particular, a full exact solution is derived within the inhomogeneous Szekeres-Szafron…