Loop Variables and Gauge Invariance in (Open) Bosonic String Theory

We give a simplified and more complete description of the loop variable approach for writing down gauge invariant equations of motion for the fields of the open string. A simple proof of gauge invariance to all orders is given. In terms of loop variables, the interacting equations look exactly like the free equations, but with a loop variable depending on an extra parameter, thus making it a band of finite width. The arguments for gauge invariance work exactly as in the free case. We show that these equations are Wilsonian RG equations with a finite world-sheet cutoff and that in the infrared limit, equivalence with the Callan-Symanzik $\beta$-functions should ensure that they reproduce the on-shell scattering amplitudes in string theory. It is applied to the tachyon-photon system and the general arguments for gauge invariance can be easily checked to the order calculated. One can see that when there is a finite world sheet cutoff in place, even the U(1) invariance of the equations for the photon, involves massive mode contributions. A field redefinition involving the tachyon is required to get the gauge transformations of the photon into standard form.Comment: 20 pages, Late

Loop Variables with Chan-Paton Factors

The Loop Variable method that has been developed for the U(1) bosonic open string is generalized to include non-Abelian gauge invariance by incorporating "Chan-Paton" gauge group indices. The scale transformation symmetry $k(s) \to k(s) \lambda (s)$ that was responsible for gauge invariance in the U(1) case continues to be a symmetry. In addition there is a "rotation" symmetry. Both symmetries crucially involve the massive modes. However it is plausible that only a linear combination, which is the usual Yang-Mills transformation on massless fields, has a smooth (world sheet) continuum limit. We also illustrate how an infinite number of terms in the equation of motion in the cutoff theory add up to give a term that has a smooth continuum limit, and thus contributes to the low energy Yang-Mills equation of motion.Comment: One paragraph has been modified and the connection with the Renormalization Group is explaine

Holomorphic Factorization and Renormalization Group in Closed String Theory

The prescription of Kawai, Lewellen and Tye for writing the closed string tree amplitudes as sums of products of open string tree amplitudes, is applied to the world sheet renormalization group equation. The main point is that regularization of the Minkowski (rather than Euclidean) world sheet theory allows factorization into left-moving and right-moving sectors to be maintained. Explicit calculations are done for the tachyon and the (gauge-fixed) graviton.Comment: 19 pages, Latex File, 9 figure

Exact C=1 Boundary Conformal Field Theories

We present a solution of the problem of a free massless scalar field on the half line interacting through a periodic potential on the boundary. For a critical value of the period, this system is a conformal field theory with a non-trivial and explicitly calculable S-matrix for scattering from the boundary. Unlike all other exactly solvable conformal field theories, it is non-rational ({\it i.e.} has infinitely many primary fields). It describes the critical behavior of a number of condensed matter systems, including dissipative quantum mechanics and of barriers in ``quantum wires''.Comment: harvmac, 10 pages, PUPT-1432/IASSNS-HEP-93/7

Topological-charge anomalies in supersymmetric theories with domain walls

Domain walls in 1+2 dimensions are studied to clarify some general features of topological-charge anomalies in supersymmetric theories, by extensive use of a superfield supercurrent. For domain walls quantum modifications of the supercharge algebra arise not only from the short-distance anomaly but also from another source of long-distance origin, induced spin in the domain-wall background, and the latter dominates in the sum. A close look into the supersymmetric trace identity, which naturally accommodates the central-charge anomaly and its superpartners, shows an interesting consequence of the improvement of the supercurrent: Via an improvement the anomaly in the central charge can be transferred from induced spin in the fermion sector to an induced potential in the boson sector. This fact reveals a dual character, both fermionic and bosonic, of the central-charge anomaly, which reflects the underlying supersymmetry. The one-loop superfield effective action is also constructed to verify the anomaly and BPS saturation of the domain-wall spectrum.Comment: 8 pages, Revte

Dynamics of Extremal Black Holes

Particle scattering and radiation by a magnetically charged, dilatonic black hole is investigated near the extremal limit at which the mass is a constant times the charge. Near this limit a neighborhood of the horizon of the black hole is closely approximated by a trivial product of a two-dimensional black hole with a sphere. This is shown to imply that the scattering of long-wavelength particles can be described by a (previously analyzed) two-dimensional effective field theory, and is related to the formation/evaporation of two-dimensional black holes. The scattering proceeds via particle capture followed by Hawking re-emission, and naively appears to violate unitarity. However this conclusion can be altered when the effects of backreaction are included. Particle-hole scattering is discussed in the light of a recent analysis of the two-dimensional backreaction problem. It is argued that the quantum mechanical possibility of scattering off of extremal black holes implies the potential existence of additional quantum numbers - referred to as ``quantum whiskers'' - characterizing the black hole.Comment: 31 page

Kaluza-Klein Black Holes in String Theory

Exact solutions of heterotic string theory corresponding to four-dimensional magnetic black holes in $N=4$ supergravity are described. The solutions describe the black holes in the throat limit, and consist of a tensor product of an $SU(2)$ WZW orbifold with the linear dilaton vacuum, supersymmetrized to $(1,0)$ world sheet SUSY. One dimension of the $SU(2)$ model is interpreted as a compactified fifth dimension, leading to a four dimensional solution with a Kaluza-Klein gauge field having a magnetic monopole background; this corresponds to a solution in $N=4$ supergravity, since that theory is obtained by dimensional reduction of string theory.Comment: 13p. uses Harvma

Classical moduli O(α′)O(\alpha') hair

We extend existing treatments of black hole solutions in String Gravity to include moduli fields. We compute the external moduli and dilaton hair, as well as of their associated axions,to $O(\alpha')$ in the framework of the loop corrected superstring effective action for a Kerr-Newman black hole background.Comment: 11 pages,LaTex file,no figure

Ultra-violet Behavior of Bosonic Quantum Membranes

We treat the action for a bosonic membrane as a sigma model, and then compute quantum corrections by integrating out higher membrane modes. As in string theory, where the equations of motion of Einstein's theory emerges by setting $\beta = 0$, we find that, with certain assumptions, we can recover the equations of motion for the background fields. Although the membrane theory is non-renormalizable on the world volume by power counting, the investigation of the ultra-violet behavior of membranes may give us insight into the supersymmetric case, where we hope to obtain higher order M-theory corrections to 11 dimensional supergravity.Comment: 25 pages, Latex, no figure

Gravitational Radiation from Travelling Waves on D-Strings

Boundary states that preserve supersymmetry are constructed for fractional D-strings with travelling waves on a ${\bf C}^3/ {{\bf Z}_2\times {\bf Z}_2}$ orbifold. The gravitational radiation emitted between two D-strings with antiparallel travelling waves is calculated.Comment: improvements and correction