Tachyon Scalar Field Research Articles

A tale of two superpotentials: Stability and instability in designer gravity

We investigate the stability of asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass at or slightly above the Breitenlohner-Freedman bound. The boundary conditions in these “designer gravity” theories are defined in terms of an arbitrary function W. Previous work had suggested that the energy in designer gravity is bounded below if (i) W has a global minimum and (ii) the scalar potential admits a superpotential P. More recently, however, certain solutions were found (numerically) to violate the proposed energy bound. We resolve the discrepancy by observing that a given scalar potential can admit two possible branches of the corresponding superpotential, P±. When there is a P- branch, we rigorously prove a lower bound on the energy; the P+ branch alone is not sufficient. Our numerical investigations (i) confirm this picture, (ii) confirm other critical aspects of the (complicated) proofs, and (iii) suggest that the existence of P- may in fact be necessary (as well as sufficient) for the energy of a designer gravity theory to be bounded below

Erratum: Energy bounds in designer gravity [Phys. Rev. D74, 064006 (2006)

We consider asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass at or slightly above the Breitenlohner-Freedman bound in d greater than or equal to 4 spacetime dimensions. The boundary conditions in these ``designer gravity'' theories are defined in terms of an arbitrary function W. We give a general argument that the Hamiltonian generators of asymptotic symmetries for such systems will be finite, and proceed to construct these generators using the covariant phase space method. The direct calculation confirms that the generators are finite and shows that they take the form of the pure gravity result plus additional contributions from the scalar fields. By comparing the generators to the spinor charge, we derive a lower bound on the gravitational energy when i) W has a global minimum, ii) the Breitenlohner-Freedman bound is not saturated, and iii) the scalar potential V admits a certain type of "superpotential."

Nonlinear equations for p-adic open, closed, and open-closed strings

We investigate the structure of solutions of boundary value problems for a one-dimensional nonlinear system of pseudodifferential equations describing the dynamics (rolling) of p-adic open, closed, and open-closed strings for a scalar tachyon field using the method of successive approximations. For an open-closed string, we prove that the method converges for odd values of p of the form p=4n+1 under the condition that the solution for the closed string is known. For p=2, we discuss the questions of the existence and the nonexistence of solutions of boundary value problems and indicate the possibility of discontinuous solutions appearing.

Energy bounds in designer gravity

We consider asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass at or slightly above the Breitenlohner-Freedman bound in d{>=}4 spacetime dimensions. The boundary conditions in these ''designer gravity'' theories are defined in terms of an arbitrary function W. We give a general argument that the Hamiltonian generators of asymptotic symmetries for such systems will be finite, and proceed to construct these generators using the covariant phase space method. The direct calculation confirms that the generators are finite and shows that they take the form of the pure gravity result plus additional contributions from the scalar fields. By comparing the generators to the spinor charge, we derive a lower bound on the gravitational energy when W has a global minimum and the Breitenlohner-Freedman bound is not saturated.

Cosmological tachyon from cubic string field theory

The classical dynamics of the tachyon scalar field of cubic string field theory is considered on a cosmological background. Starting from a nonlocal action with arbitrary tachyon potential, which encodes the bosonic and several supersymmetric cases, we study the equations of motion in the Hamilton-Jacobi formalism and with a generalized Friedmann equation, appliable in braneworld or modified gravity models. The cases of cubic (bosonic) and quartic (supersymmetric) tachyon potential in general relativity are automatically included. We comment the validity of the slow-roll approximation, the stability of the cosmological perturbations, and the relation between this tachyon and the Dirac-Born-Infeld one.

Inflation from D3-brane motion in the background of D5-branes

We study inflation arising from the motion of a Bogomol'nyi-Prasad-Sommerfield D3-brane in the background of a stack of $k$ parallel D5-branes. There are two scalar fields in this setup: (i) the radion field $R$, a real scalar field, and (ii) a complex tachyonic scalar field $\ensuremath{\chi}$ living on the world volume of the open string stretched between the D3 and D5 branes. We find that inflation is realized by the potential of the radion field, which satisfies observational constraints coming from the cosmic microwave background. After the radion becomes of the order of the string length scale ${l}_{s}$, the dynamics is governed by the potential of the complex scalar field. Since this field has a standard kinematic term, reheating can be successfully realized by the mechanism of tachyonic preheating with spontaneous symmetry breaking.

The equation of the -adic open string for the scalar tachyon field

We study the structure of solutions of the one-dimensional non-linear pseudodifferential equation describing the dynamics of the -adic open string for the scalar tachyon field . We explain the role of real zeros of the entire function and the behaviour of solutions in the neighbourhood of these zeros. We point out that discontinuous solutions can appear if is even. We use the method of expanding the solution and the function in Hermite polynomials and modified Hermite polynomials and establish a connection between the coefficients of these expansions (integral conservation laws). For we construct an infinite system of non-linear equations in the unknown Hermite coefficients and study its structure. We consider the 3-approximation. We indicate a connection between the problems stated and a non-linear boundary-value problem for the heat equation.

Note on the decay of noncommutative solitons

We propose an ansatz for the equations of motion of the noncommutative model of a tachyonic scalar field interacting with a gauge field, which allows one to find time-dependent solutions describing decaying solitons. These correspond to the collapse of lower dimensional branes obtained through tachyon condensation of unstable brane systems in string theory.

Cosmology with tachyon field as dark energy

We present a detailed study of cosmological effects of homogeneous tachyon matter coexisting with nonrelativistic matter and radiation, concentrating on the inverse square potential and the exponential potential for the tachyonic scalar field. A distinguishing feature of these models (compared to other cosmological models) is that the matter density parameter and the density parameter for tachyons remain comparable even in the matter dominated phase. For the exponential potential, the solutions have an accelerating phase, followed by a phase with $a(t)\ensuremath{\propto}{t}^{2/3}$ as $\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{\infty}.$ This eliminates the future event horizon present in cold dark matter models with a cosmological constant $(\ensuremath{\Lambda}\mathrm{CDM})$ and is an attractive feature from the string theory perspective. A comparison with supernova type Ia data shows that for both the potentials there exists a range of models in which the universe undergoes an accelerated expansion at low redshifts which are also consistent with the requirements of structure formation. They do require fine-tuning of parameters but not any more than in the case of $\ensuremath{\Lambda}\mathrm{CDM}$ models or quintessence models.

Comments on Quantum Field Theory of Tachyons

The problem of tachyons is investigated within the framework of quantum field theory. The quantization methods for a free scalar tachyon field, which have so far been proposed by various authors, are critically reviewed. Among them the Arons-Sudarshan method is found to be most satisfactory, which guarantees at least the relativistic covariance of the theory at the expense of locality and reasonable energy spectrum. On the basis of this method, interactions of a tachyon field are investigated. It is found that causal S-matrices do not exist as far as interaction terms are restricted to the ordinary, local-polynomial type. A model S-matrix, which is unitary but not causal, is then assumed, and the reinterpretation principle is applied to it in order to remove states of negative-energy tachyons. It is found that the reinterpreted S-matrix thus obtained is not consistent with unitarity. Physical reality of particles that can travel faster than light, or tachyons as they are called nowadays, has long remained in doubt, and until very recently related problems have not attracted any serious attention of physicists. The reason for such neglect, as is well known, lies in its apparent contradiction with causality in the most naive sense of the word, that is, effect should be preceded by cause. Suppose that in a certain frame of reference there is a tachyon travel­ ling with positive energy and forwards in time. When observed from another frame of reference, it looks as if the particle were travelling with negative energy and backwards in time, so that cause appears to be preceded by effect. In their recent paper, Bilaniuk, Deshpande and Sudarshan 1 ) have suggested, however, a theoretical possibility of removing the above contradiction by introduc­ ing the so-called reinterpretation principle. According to this principle, a tachyon travelling with negative energy and backwards in time is interpreted as the one travelling with positive energy and forwards in time, causality being thereby re­