Tachyon Background Research Articles

Instantons in sine-Liouville theory

We compute instanton corrections to the partition function of sine-Liouville (SL) theory, which provides a worldsheet description of two-dimensional string theory in a non-trivial tachyon background. We derive these corrections using a matrix model formulation based on a chiral representation of matrix quantum mechanics and using string theory methods. In both cases we restrict to the leading and subleading orders in the string coupling expansion. Then the CFT technique is used to compute two orders of the expansion in the SL perturbation parameter λ, while the matrix model gives results which are non-perturbative in λ. The matrix model results perfectly match those of string theory in the small λ expansion. We also generalize our findings to the case of perturbation by several tachyon vertex operators carrying different momenta, and obtain interesting analytic predictions for the disk two-point and annulus one-point functions with ZZ boundary condition.

Brane with transverse rotation and background fields: boundary state and tachyon condensation

The boundary state corresponding to the Dp-brane with a transverse rotation in the presence of the Kalb–Ramond and tachyon background fields and a U(1) internal field will be constructed. We shall investigate effects of the open string tachyon condensation on this brane via its boundary state. We demonstrate that the background fields and transverse rotation cannot protect the brane against the collapse. Our calculations are in the context of the bosonic string theory.

Holographic beta functions for the generalized sine-Gordon theory

The Sine Gordon theory is generalized to include several cosine terms. This is similar to the world sheet description of a string propagating in a tachyon background. This model is studied as a (boundary) 2d euclidean field theory and also using an $AdS_3$ holographic bulk dual. The beta functions for the cosine vertex of this modified theory are first computed in the boundary using techniques based on the exact RG. The beta functions are also computed holographically using position space and momentum space techniques. The results are in agreement with each other and with earlier computations. The beta functions of the field strength renormalization are computed in position space. They match with the earlier results in \cite{Oak:2017trw}.

Integrability of type 0A matrix model in the presence of D-brane

We consider type 0A matrix model in the presence of spacelike D-brane which is localized in matter direction at any arbitrary point. In string theory, the boundary state, which in matrix model corresponds to the Laplace transform of the macroscopic loop operator, is known to obey the operator constraints corresponding to open string boundary condition. When we analyze MQM as well as the respective collective field theory and compare it with dual string theory, it appears that consistency of the theory requires a condition equivalent to a constraint on the matter part that needed to be imposed in the matrix model. We identified this condition and observed that this results in constraining the macroscopic loop operator so that it projects the Hilbert space generated by the operator to its physical sector at the point of insertion while keeping the bulk matrix model unaffected, thereby describing a situation parallel to string theory. We analyzed the theory with uncompactified time and have shown explicitly that the matrix model predictions are in good agreement with the relevant string theory. Next, we considered the theory with compactified time, analyzed MQM on a circle in the presence of D-brane. We evaluated the partition function along with the constrained macroscopic loop operator in the grand canonical ensemble and showed the free energy corresponds to that of a deformed Fermi surface. We have also shown that the path integral in the presence of D-brane can be expressed as the Fredholm determinant. We have studied the fermionic scattering in a semiclassical regime. Finally, we considered the compactified theory in the presence of the D-brane with tachyonic background. We evaluated the free energy in the grand canonical ensemble. We have shown the integrable structure of the respective partition function and it corresponds to the tau function of Toda hierarchy. We have also analyzed the dispersionless limit.

Investigation of zero-modes for a dynamical Dp-brane

In this article, we investigate zero-modes for a dynamical (rotating-moving) Dp-brane, coupled to the electromagnetic and tachyonic background fields. This work is done by the boundary state methods, in three cases of bosonic and fermionic boundary states and superstring partition function. By analyzing the obtained zero-modes in either of the cases, interesting results will be obtained. Our findings demonstrate the importance of the zero-mode and its effects on the background fields and the defined internal properties of the described system.

Some special features of a rotating-moving Dp-brane

Using the boundary string field theory (BSFT) techniques we study the boundary state and partition function for a dynamical (rotating-moving) Dp-brane coupled to the electromagnetic and tachyonic background fields in superstring theory. By making use of the created partition function, the super BSFT action with a tachyonic field and Dirac-Born-Infeld–type action will be constructed. By analyzing the obtained action interesting features will be revealed.

Tachyon field theory description of (thermo)dynamics in dS space

In this work, we present a few pieces of evidence in support of a possible connection of the gravitational theory in dS space to the worldvolume theory of unstable D-branes. We show that the action describing the geodesic motion of a massive particle (or point-like object) in static dS space turns out to be the same as that of the tachyon field theory for an unstable particle. The motion along the radial direction from the origin, a locally Minkowski spacetime, to the horizon, a locally Rindler space times a sphere, represents just the tachyon condensation process, therefore providing a geometric picture of tachyon condensation. We further study a scalar in global or flat dS and the tachyon fluctuations in a homogeneous tachyon background, representing either the full or half S-brane, on unstable D-branes and find that certain dynamics of the dS universe corresponds to that of the homogeneous full or half S-brane. The thermal temperature of tachyon radiation is found to agree with that felt by any timelike observer in dS space. In string theory context, this temperature is just the Hagedorn one, signaling a phase transition to closed strings. An understanding of this transition in the bulk dS space is also given.

Tachyon condensation on a nonstationaryDp-brane with background fields in superstring theory

Using the boundary state formalism we obtain the partition function corresponding to a dynamical (rotating-moving) D$p$-brane in the presence of electromagnetic and tachyonic background fields in the superstring theory. The instability of such D$p$-brane due to the tachyon condensation is investigated.

High-energy asymptotics of D-brane decay amplitudes from Coulomb gas electrostatics

We study the high-energy limit of tree-level string production amplitudes from decaying D-branes in bosonic string theory, interpreting the vertex operators as external charges interacting with a Coulomb gas corresponding to the rolling tachyon background, and performing an electrostatic analysis. In particular, we consider two open string - one closed string amplitudes and four open string amplitudes, and calculate explicit formulas for the leading exponential behavior.

Dark energy as an off-shell tachyon background in four-dimensional strings

We consider a time-dependent bosonic string in graviton, dilaton and tachyon backgrounds, for which it was already shown that conformal invariance is respected to all orders in α′ and in any space–time dimension. Assuming that the tachyon is off-shell, we show in this note that the specific time-homogeneity of the corresponding space–time effective action leads to a power-law expanding Universe, that can be interpreted as dark energy. We arrive at this result without requiring the knowledge of the structure of the string effective action, which is not known to all orders in α′. Moreover, in our approach, the background configurations are consistent in a four-dimensional space–time, without any need for extra dimensions.

String scattering amplitudes from Dyson gas

In this note we review the relation between the open string rolling tachyon background and a classical two-dimensional Coulomb gas on a circle – the Dyson gas. Open string n -point amplitudes directly relate to adding external charges on the Dyson gas ensemble. By calculating the grand canonical partition function of the Dyson with external charges we find an approximation formula for the string amplitude. This note is based on the work with M. Jarvinen and Esko Keski-Vakkuri, eprint arXiv:0806.1491 .

Energy-momentum tensor of perturbed tachyon matter

We add an initial nonhomogeneous perturbation to an otherwise homogeneous condensing tachyon background and compute its spacetime energy-momentum tensor from world-sheet string theory. We show that in the far future the energy-momentum tensor corresponds to nonhomogeneous pressureless tachyon matter.

Tachyon-Dilaton-induced inflation as an α′-resummed string background

Within the framework of a novel functional method on the world-sheet of the string, we discuss simple but re-summed (in the Regge slope) inflationary scenarios in the context of closed Bosonic strings, living in four target-space dimensions, in the presence of non-trivial tachyon, dilaton and graviton cosmological backgrounds. The inflationary solutions are argued to guarantee the vanishing of the corresponding Weyl anomaly coefficients in a given world-sheet renormalization scheme, thereby ensuring conformal invariance of the corresponding σ-model to all orders in the Regge slope. The key property is the requirement of ``homogeneity'' of the corresponding Weyl anomaly coefficients. Inflation entails appropriate relations between the dilaton and tachyon field configurations, whose form can lead to either a de Sitter vacuum, incompatible though (due to the cosmic horizons) with the perturbative string scattering amplitudes, or to cosmic space-times involving brief inflationary periods, interpolating smoothly between power-law and/or Minkowski Universes. The latter situation is characterized by well-defined scattering amplitudes, and is thus compatible with a perturbative string framework. It is this scenario that we consider a self-consistent ground state in our framework, which is based on local field redefinitions of background fields.

Thermodynamic interpretation of time for superstring rolling tachyons

Rolling tachyon backgrounds, arising from open strings on unstable branes in bosonic string theory, can be related to a simple statistical mechanical model-Coulomb gas of point charges in two dimensions confined to a circle, the Dyson gas. In this paper we describe a statistical system that is dual to non-BPS branes in superstring theory. We argue that even though the concept of time is absent in the statistical dual sitting at equilibrium, the notion of time can emerge at the large number of particles $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit.

Thermodynamic interpretation of time for rolling tachyons

We show that the open string worldsheet description of brane decay (discussing a specific example of a rolling tachyon background) can be related to a sequence of points of thermodynamic equilibrium of a grand canonical ensemble of point charges on a circle, the Dyson gas. Subsequent instants of time are related to neighboring values of the chemical potential or the average particle number $\overline{N}$. The free energy of the system decreases in the direction of larger $\overline{N}$ or later times, thus defining a thermodynamic arrow of time. Time evolution equations are mapped to differential equations relating thermal expectation values of certain observables at different points of thermal equilibrium. This suggests some lessons concerning emergence of time from an underlying microscopic structure in which the concept of time is absent.

CFT for Closed String Tachyon Condensation

We construct a class of CFT's which describe space-dependent closed string tachyon backgrounds, as the IR limit of GLSM's in which the FI-parameter is promoted to a superfield. Whole process of tachyon condensation is described by a single CFT. We apply this construction to several examples, in which target space is deformed drastically, and the dilaton background may vary, as a tachyon condenses.

Superstring disk amplitudes in a rolling tachyon background

We study the tree level scattering or emission of $n$ closed superstrings from a decaying non-BPS brane in Type II superstring theory. We attempt to calculate generic $n$-point superstring disk amplitudes in the rolling tachyon background. We show that these can be written as infinite power series of Toeplitz determinants, related to expectation values of a periodic function in Circular Unitary Ensembles. Further analytical progress is possible in the special case of bulk-boundary disk amplitudes. These are interpreted as probability amplitudes for emission of a closed string with initial conditions perturbed by the addition of an open string vertex operator. This calculation has been performed previously in bosonic string theory, here we extend the analysis for superstrings. We obtain a result for the average energy of closed superstrings produced in the perturbed background.

The tachyon at the end of the universe

We show that a tachyon condensate phase replaces the spacelike singularity in certain cosmological and black hole spacetimes in string theory. We analyze explicitly a set of examples with flat spatial slices in various dimensions which have a winding tachyon condensate, using worldsheet path integral methods from Liouville theory. In a vacuum with no excitations above the tachyon background in the would-be singular region, we analyze the production of closed strings in the resulting state in the bulk of spacetime. We find a thermal result reminiscent of the Hartle-Hawking state, with tunably small energy density. The amplitudes exhibit a self-consistent truncation of support to the weakly-coupled small-tachyon region of spacetime. We argue that the background is accordingly robust against back reaction, and that the resulting string theory amplitudes are perturbatively finite, indicating a resolution of the singularity and a mechanism to start or end time in string theory. Finally, we discuss the generalization of these methods to examples with positively curved spatial slices.

Energy quantisation in bulk bouncing tachyon

We argue that the closed string energy in the bulk bouncing tachyon background is to be quantised in a simple manner as if strings were trapped in a finite time interval. We discuss it from three different viewpoints; (1) the timelike continuation of the sinh-Gordon model, (2) the dual matrix model description of the (1+1)-dimensional string theory with the bulk bouncing tachyon condensate, (3) the c_L=1 limit of the timelike Liouville theory with the dual Liouville potential turned on. There appears to be a parallel between the bulk bouncing tachyon and the full S-brane of D-brane decay. We find the critical value \lambda_c of the bulk bouncing tachyon coupling which is analogous to \lambda_o=1/2 of the full S-brane coupling, at which the system is thought to be at the bottom of the tachyon potential.

Boundary Liouville theory atc= 1

The c=1 Liouville theory has received some attention recently as the Euclidean version of an exact rolling tachyon background. In an earlier paper it was shown that the bulk theory can be identified with the interacting c=1 limit of unitary minimal models. Here we extend the analysis of the c=1-limit to the boundary problem. Most importantly, we show that the FZZT branes of Liouville theory give rise to a new 1-parameter family of boundary theories at c=1. These models share many features with the boundary Sine-Gordon theory, in particular they possess an open string spectrum with band-gaps of finite width. We propose explicit formulas for the boundary 2-point function and for the bulk-boundary operator product expansion in the c=1 boundary Liouville model. As a by-product of our analysis we also provide a nice geometric interpretation for ZZ branes and their relation with FZZT branes in the c=1 theory.