Joseph A. Minahan

The Bethe-ansatz for Script N = 4 super Yang-Mills

We derive the one loop mixing matrix for anomalous dimensions in N=4 Super Yang-Mills. We show that this matrix can be identified with the Hamiltonian of an integrable SO(6) spin chain with vector sites. We then use the Bethe ansatz to find a recipe for computing anomalous dimensions for a wide range of operators. We give exact results for BMN operators with two impurities and results up to and including first order 1/J corrections for BMN operators with many impurities. We then use a result of Reshetikhins to find the exact one-loop anomalous dimension for an SO(6) singlet in the limit of large bare dimension. We also show that this last anomalous dimension is proportional to the square root of the string level in the weak coupling limit.

Circular semiclassical string solutions on AdS5×S5

We discuss two semiclassical string solutions on AdS5×S5. In the first case, we consider a multiwrapped circular string pulsating in the radial direction of AdS5, but fixed to a point on the S5. We compute the energy of this motion as a function of a large quantum number n. We identify the string level with mn, where m is the number of string wrappings. Using the AdS/CFT correspondence, we argue that the bare dimension of the corresponding gauge invariant operator is 2n and that its anomalous dimension scales as λ1/4mn, for large n. Next we consider a multiwrapped circular string pulsating on the S5. We compute the energy of this motion as a function of a large quantum number, n where again the string level is given as mn. We find that the dimension of the corresponding operator is 2n(1+f(m2λ/(2n)2)), where f(x) is computible as a series about x=0 and where it is analytic. We also compare this result to the BMN result for large J operators.

Effective tachyon dynamics in superstring theory

A recently proposed l = ∞ field theory model of tachyon dynamics for unstable bosonic D-branes has been shown to arise as the two-derivative truncation of (boundary)-string field theory. Using an l→∞ limit appropriate to stable kinks we obtain a model for the tachyon dynamics on unstable D-branes or D-brane anti-D-brane pairs of superstring theory. The tachyon potential is a positive definite even function of the tachyon, and at the stable global minima there is no on-shell dynamics. The kink solution mimics nicely the properties of stable D-branes: the spectrum of the kink consists of infinite levels starting at zero mass, with spacing double the value of the tachyon mass-squared. It is natural to expect that this model will arise in (boundary) superstring field theory.

Rolling the tachyon in super BSFT

We investigate the rolling of the tachyon on the unstable D9 brane in type IIA string theory by studying the BSFT action. The action is known for linear profiles of the tachyon, which is the expected asymptotic behavior of the tachyon as it approaches the closed string vacuum, as recently described by Sen. Making a rather strong assumption about the extrapolation of this action to a lagrangian, we find consistentency with the general Sen description, in that it implies a constant energy density with diminishing pressure. However, the details are somewhat different from an effective field theory of Born-Infeld type. For instance, the BSFT action implies there are poles for certain rolling velocities, while a Born-Infeld action would have a cut. We also find that solutions with pressure diminishing from either the positive or negative side are possible.

One-loop amplitudes on orbifolds and the renormalization of coupling constants

Abstract We consider three-point one-loop amplitudes for strings propagating on orbifolds that preserve a supersymmetry. For three external gauge bosons, we compute the explicit wave-function renormalization of the external legs and show that it leads to the correct value for the Yang-Mills β-function. For two gauge bosons and a graviton, we show that there is no renormalization of the coupling, but if the graviton is replaced with an antisymmetric tensor, then the coupling is renormalized.

Field theory models for tachyon and gauge field string dynamics

In hep-th/0008227, the unstable lump solution of 3 theory was shown to have a spectrum governed by the solvable Schroedinger equation with the l = 3 reflectionless potential and was used as a model for tachyon condensation in string theory. In this paper we study in detail an l→∞ scalar field theory model whose lump solution mimics remarkably the string theory setup: the original field theory tachyon and the lump tachyon have the same mass, the spectrum of the lump consists of equally spaced infinite levels, there is no continuous spectrum, and nothing survives after tachyon condensation. We also find exact solutions for lumps with codimension ≥ 2, and show that that their tensions satisfy (1/2π)(Tp/Tp+1) = e/√(2π) ≈ 1.08. We incorporate gauge fixed couplings to a U(1) gauge field which preserve solvability and result in massless gauge fields on the lump.

Finite size effects for giant magnons on physical strings

Using finite gap methods, we find the leading order finite size corrections for an arbitrary number of giant magnons on physical strings, where the sum of the momenta is a multiple of 2π. Our results are valid for the Hofman–Maldacena fundamental giant magnons as well as their dyonic generalizations. The energy corrections turn out to be surprisingly simple, especially if all the magnons are fundamental, and at leading order are independent of the magnon flavors. We also show how to use the Bethe ansatz to find finite size corrections for dyonic giant magnons with large R-charges.

Gauge fields and fermions in tachyon effective field theories

In this paper we incorporate gauge fields into the tachyon field theory models for unstable D-branes in bosonic and in type-II string theories. The chosen couplings yield massless gauge fields and an infinite set of equally spaced massive gauge fields on codimension one branes. A lack of a continuum spectrum is taken as evidence that the stable tachyon vacuum does not support conventional gauge excitations. For the bosonic string model we find two possible solvable couplings, one closely related to Born-Infeld forms and the other allowing a detailed comparison to the open string modes on bosonic D-branes. We also show how to include fermions in the type-II model. They localize correctly on stable codimension one branes resulting in bose-fermi degeneracy at the massless level. Finally, we establish the solvability of a large class of models that include kinetic terms with more than two derivatives.

Mode interactions of the tachyon condensate in p-adic string theory

We study the fluctuation modes for lump solutions of the tachyon effective potential in p-adic open string theory. We find a discrete spectrum with equally spaced mass squared levels. We also find that the interactions derived from this field theory are consistent with p-adic string amplitudes for excited string states.

Asymptotic freedom and confinement from type 0 string theory

We argue that there are generic solutions to the type 0 gravity equations of motion that are confining in the infrared and have log scaling in the ultraviolet. The background curvature generically diverges in the IR. Nevertheless, there exist solutions where higher order string corrections appear to be exponentially suppressed in the IR with respect to the leading type 0 gravity terms. For these solutions the tachyon flows to a fixed value. We show that the generic solutions lead to a long range linear quark potential, magnetic screening and a discrete glueball spectrum. We also estimate some WKB glueball mass ratios and compare them to ratios found using finite temperature models and lattice computations.