Gauge String Research Articles

String Gauge Symmetries in the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of Background Gauge Fields

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world- sheet time σ0 = τ = constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time . The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field or in the presence of gauge field and the constant scalar axion field , then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino/Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

Heavy quarks in the presence of higher derivative corrections from AdS/CFT

We use the gauge–string duality to study heavy quarks in the presence of higher derivative corrections. These corrections correspond to the finite-coupling corrections on the properties of heavy quarks in a hot plasma. In particular, we study the effects of these corrections on the energy loss and the dissociation length of a quark–antiquark pair. We show that the calculated energy loss of heavy quarks through the plasma increases. We also find in general that the dissociation length becomes shorter with the increase of coupling parameters of higher curvature terms.

Scattering of giant holes

We study scalar excitations of high spin operators in N=4 super Yang-Mills theory, which are dual to solitons propagating on a long folded string in AdS_3 x S^1. In the spin chain description of the gauge theory, these are associated to holes in the magnon distribution in the sl(2,R) sector. We compute the all-loop hole S-matrix from the asymptotic Bethe ansatz, and expand in leading orders at weak and strong coupling. The worldsheet S-matrix of solitonic excitations on the GKP string is calculated using semiclassical quantization. We find an exact agreement between the gauge theory and string theory results.

Closed string cohomology in open string field theory

We show that closed string states in bosonic string field theory are encoded in the cyclic cohomology of cubic open string field theory (OSFT) which, in turn, classifies the deformations of OSFT. This cohomology is then shown to be independent of the open string background. Exact elements correspond to closed string gauge transformations, generic boundary deformations of Witten’s 3-vertex and infinitesimal shifts of the open string background. Finally it is argued that the closed string cohomology and the cyclic cohomology of OSFT are isomorphic to each other.

Amplitudes in Noncritical Dimensions and Dimensional Regularization

We study how the dimensional regularization works in the light-cone gauge string field theory. We show that it is not necessary to add a contact term to the string field theory action as a counter term in this regularization at least at the tree level. We also investigate the one-loop amplitudes of the bosonic theory in noncritical dimensions and show that they are modular invariant.

Light-cone gauge NSR strings in noncritical dimensions II — Ramond sector

Light-cone gauge superstring theory in noncritical dimensions corresponds to a worldsheet theory with nonstandard longitudinal part in the conformal gauge. The longitudinal part of the worldsheet theory is a superconformal field theory called X^{\pm} CFT. We show that the X^{\pm} CFT combined with the super-reparametrization ghost system can be described by free variables. It is possible to express the correlation functions in terms of these free variables. Bosonizing the free variables, we construct the spin fields and BRST invariant vertex operators for the Ramond sector in the conformal gauge formulation. By using these vertex operators, we can rewrite the tree amplitudes of the noncritical light-cone gauge string field theory, with external lines in the (R,R) sector as well as those in the (NS,NS) sector, in a BRST invariant way.

Light-Cone Gauge String Field Theory and Dimensional Regularization

We review our recent proposals to dimensionally regularize the light-cone gauge string field theory.

Acoustical differences between treble guitar strings of different tension (i.e., gauge).

The thickness of a guitar string has a complicated effect on the overall sound of the instrument, affecting the degree of inharmonicity in the tone. [Fletcher et al., (1991).] Different players also select strings of certain tensions because of their perceived qualities such as brightness and loudness. The acoustical differences in the sound and sustain of plucked nylon guitar strings as a function of string tension were measured in an effort to quantify these differences. The open string, fifth-fret, and 12th-fret harmonic waveforms of the treble (G, B, and E) strings were studied for sets of strings with different tensions. Only treble strings, made of a monofilament pure nylon strand, were studied. The levels of the first ten harmonics relative to the level of the fundamental were measured for each sound on each string, as well as the duration of the sustain in each case. Patterns in the sustain times and spectra as a function of string gauge will be presented. [Research supported by the Richard Stockton College of New Jersey.]

Rotating mesons in the presence of higher derivative corrections from gauge–string duality

We consider a rotating quark–antiquark ( q q ¯ ) pair in N = 4 thermal plasma. By using the AdS/CFT correspondence, the properties of this system are investigated. In particular, we study variation of a rotating string radius at the boundary as a function of its tip and angular velocity. We also extend the results to higher derivative corrections, i.e. R 2 and R 4 which correspond to finite coupling corrections on the rotating quark–antiquark system in the hot plasma. In the R 4 case and for fixed angular velocity the string endpoints become more and more separated as λ − 1 decreases. To study R 2 corrections, rotating quark–antiquark system in Gauss–Bonnet background has been considered. We summarize the effects of these corrections in the conclusion section.

The banjo: Developing a plausible model from first principles.

The banjo is one of the few musical instruments which is amenable to analytical modeling. It is fundamentally two connected canonical wave bearing systems, and as such, it can be solved. Furthermore, the requisite computer code runs quickly, making it practical to examine the instrument’s response as functions of a variety of parameters. The parameters are the things banjo players tweek in their attempt to get the sound they want; things like head tension, bridge mass, and string gauge. This tutorial will start with first principles in both the physics and the mathematics and end with movies of the calculated head response and radiated sound as functions of time and frequency. Numerical models can never be exact. Real systems, and particularly musical instruments, are just too complex for this, but models can provide useful guidance by illuminating what might happen as parameters are changed.

Light-cone gauge string field theory in noncritical dimensions

We study light-cone gauge string field theory in noncritical space-time dimensions. Such a theory corresponds to a string theory in a Lorentz noninvariant background. We identify the worldsheet theory for the longitudinal coordinate variables X± and study its properties. It is a CFT with the right value of Virasoro central charge, using which we propose a BRST invariant formulation of the worldsheet theory.

Gauge threshold corrections for local type-IIB/F-theory GUTs

We study gauge threshold corrections for local GUT models in IIB/F-theory. Consistency with holomorphy requirements of supergravity and the Kaplunovsky-Louis formula implies that the unification scale is enhanced by the bulk radius R from the string scale to M_X =RM_S. We argue that the stringy interpretation of this is via a locally uncancelled tadpole sourced by the hypercharge flux. This sources closed string modes propagating into the bulk; equivalently open string gauge coupling running up to the winding scale M_X. The enhancement to R M_s is tied to GUT breaking by a globally trivial hypercharge flux and will occur in all models realising this mechanism.

Singular Liouville fields and spiky strings in ℝ1,2and SL(2,ℝ)

The closed string dynamics in 1,2 and SL(2,) is studied within the scheme of Pohlmeyer reduction. In both spaces two different classes of string surfaces are specified by the structure of the fundamental quadratic forms. The first class in 1,2 is associated with the standard lightcone gauge strings and the second class describes spiky strings and their conformal deformations on the Virasoro coadjoint orbits. These orbits correspond to singular Liouville fields with the monodromy matrixes ± I. The first class in SL(2,) is parameterized by the Liouville fields with vanishing chiral energy functional. Similarly to 1,2, the second class in SL(2,) describes spiky strings, related to the vacuum configurations of the SL(2,)/U(1) coset model.

IDEAS OF GEOMETRIZATION, GEOMETRIC INVARIANTS OF LOW-DIMENSIONAL MANIFOLDS, AND TOPOLOGICAL QUANTUM FIELD THEORIES

IDEAS OF GEOMETRIZATION, GEOMETRIC INVARIANTS OF LOW-DIMENSIONAL MANIFOLDS, AND TOPOLOGICAL QUANTUM FIELD THEORIES

On the Hecke algebras and the colored HOMFLY polynomial

The colored HOMFLY polynomial is the quantum invariant of oriented links in $S^3$ associated with irreducible representations of the quantum group $U_q(\mathrm{sl}_N)$. In this paper, using an approach to calculate quantum invariants of links via cabling-projection rule, we derive a formula for the colored HOMFLY polynomial in terms of the characters of the Hecke algebras and Schur polynomials. The technique leads to a fairly simple formula for the colored HOMFLY polynomial of torus links. This formula allows us to test the Labastida-Mari\~no-Vafa conjecture, which reveals a deep relationship between Chern-Simons gauge theory and string theory, on torus links.

On Schnabl solutions of string field equations

We clarify the relationship between Schnabl’s solution and pure gauge configurations. Both Schnabl’s and pure gauge solutions are obtained by means of an iterative procedure. We show that the pure gauge string field configuration that is used in the construction of a perturbation series for Schnabl’s solution diverges on a large subspace of string configurations, but it can be rendered convergent by adding a compensating term. The additional term ensures the fulfillment of the equations of motion in a weak sense. This compensating term coincides with the term necessary for obtaining an action consistent with Sen’s first conjecture.

Notes on integrability in gauge theory and string theory

This paper reviews the emergence of integrability in the context of the AdS/CFT correspondence at an introductory level. In particular, we discuss how planar supersymmetric Yang–Mills theory and free string theory on AdS5 × S5 can both be related to integrable systems in one spatial dimension. We determine the spectrum of the model in the limit of long operators/strings.

Gauge–string duality and integrability: progress and outlook

Gauge–string duality and integrability: progress and outlook

Matching gauge theory and string theory in a decoupling limit of AdS/CFT

We identify a regime of the AdS/CFT correspondence in which we can quantitatively match = 4 super Yang-Mills (SYM) for small 't Hooft coupling with weakly coupled type IIB string theory on AdS5 × S5. We approach this regime by taking the same decoupling limit on both sides of the correspondence. On the gauge theory side only the states in the SU(2) sector survive, and in the planar limit the Hamiltonian is given by the XXX1/2 Heisenberg spin chain. On the string theory side we show that the decoupling limit corresponds to a non-relativistic limit. In this limit some of the bosonic modes and all of the fermionic modes of the string become infinitely heavy and decouple. We first take the decoupling limit of the string sigma-model classically. This enables us to identify a semi-classical regime with semi-classical string states even though we are in a regime corresponding to small 't Hooft coupling. We furthermore analyze the quantum corrections that enter in taking the limit. From this we infer that gauge theory and string theory match, both in terms of the action and the spectrum, for the leading part and the first correction away from the semi-classical regime. Finally we consider the implications for the hitherto unexplained matching of the one-loop contribution to the energy of certain gauge theory and string theory states, and we explain how our results give a firm basis for the matching of the Hagedorn temperature in hep-th/0608115.

α-SYMMETRIES, COLORED DIMENSIONS AND GAUGE–STRING CORRESPONDENCE

We propose a scenario of gauge–string correspondence by relating the SU(3) color group to hidden space–time isometries originating from extra dimensions. These isometries (α-symmetries) are the special symmetries of RNS superstring theories under global nonlinear space–time transformations. The vertex operators for the octet of gluons are constructed by the procedure of "photon painting," that is, with the SU(3) subgroup of the α-symmetry generators acting on a regular open string photon, so the corresponding open string excitations are in the adjoint of SU(3). Remarkably, the operator algebra of these massless gluon vertices is closed and possesses the full zigzag symmetry, crucial for the isomorphism between open strings and QCD. As a result, the scattering amplitudes of the constructed open string vertex operators have a field-theoretic rather than a stringy structure, including the absence of standard tower of massive intermediate states. Our model also suggests that the total number of underlying hidden dimensions is three, with each extra dimension carrying its appropriate SU(3) color and anticolor.