Searcharxiv⌕ Search

arXiv subjects

B. Sathiapalan

Publications and source records attributed to B. Sathiapalan.

At least 55 records · Page 3Linked to original sources
arXiv2004

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.

hep-th↗
arXiv2004

Closed String Tachyons on C/Z_N

We analyse the condensation of closed string tachyons on the $C/Z_N$ orbifold. We construct the potential for the tachyons upto the quartic interaction term in the large $N$ limit. In this limit there are near marginal tachyons. The quartic coupling for these tachyons is calculated by subtracting from the string theory amplitude for the tachyons, the contributions from the massless exchanges, computed from the effective field theory. We argue that higher point interaction terms are are also of the same order in 1/N as the quartic term and are necessary for existence of the minimum of the tachyon potential that is consistent with earlier analysis.

hep-th↗
arXiv2003

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 $k(s) \to k(s) λ(s)$ 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.

hep-th↗
arXiv2002

Loop Variables in String Theory

The loop variable approach is a proposal for a gauge invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space-time gauge invariance rather than world-sheet properties. In essence it is a version of Wilson's exact renormalization group equation for the world sheet theory. It involves all the massive modes and is defined with a finite world-sheet cutoff, which allows one to go off the mass-shell. On shell the tree amplitudes of string theory are reproduced. The equations are gauge invariant off shell also. This article is a self-contained discussion of the loop variable approach as well as its connection with the renormalization group.

hep-th↗
arXiv2002

On the Emergence of the Microcanonical Description from a Pure State

We study, in general terms, the process by which a pure state can ``self-thermalize'' and {\em appear} to be described by a microcanonical density matrix. This requires a quantum mechanical version of the Gibbsian coarse graining that conceptually underlies classical statistical mechanics. We introduce some extra degrees of freedom that are necessary for this. Interaction between these degrees and the system can be understood as a process of resonant absorption and emission of ``soft quanta''. This intuitive picture allows one to state a criterion for when self thermalization occurs. This paradigm also provides a method for calculating the thermalization rate using the usual formalism of atomic physics for calculating decay rates. We contrast our prescription for coarse graining, which is somewhat dynamical, with the earlier approaches that are intrinsically kinematical. An important motivation for this study is the black hole information paradox.

cond-mat.stat-mech↗
arXiv2002

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 $β$-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.

hep-th↗
arXiv2001

Wave Functionals, Gauge Invariant Equations for Massive Modes and the Born-Infeld Equation in the Loop Variable Approach to String Theory

In earlier papers on the loop variable approach to gauge invariant interactions in string theory, a ``wave functional'' with some specific properties was invoked. It had the purpose of converting the generalized momenta to space time fields. In this paper we describe this object in detail and give some explicit examples. We also work out the interacting equations of the massive mode of the bosonic string, interacting with electromagnetism, and discuss in detail the gauge invariance. This is naturally described in this approach as a massless spin two field interacting with a massless spin one field in a higher dimension. Dimensional reduction gives the massive system. We also show that in addition to describing fields perturbatively, as is required for reproducing the perturbative equations, the wave functional can be chosen to reproduce the Born-Infeld equations, which are non-perturbative in field strengths. This makes contact with the sigma model approach.

hep-th↗
arXiv2000

High Temperature Limit of the $ N= 2 $ IIA Matrix Model

The high temperature limit of a system of two D-0 branes is investigated. The partition function can be expressed as a power series in $β$ (inverse temperature). The leading term in the high temperature expression of the partition function and effective potential is calculated {\em exactly}. Physical quantities like the mean square separation can also be exactly determined in the high temperature limit. We comment on SU(3) IIB matrix model and the difficulties to study it.

hep-lat↗
arXiv2000

Loop Variables and Gauge Invariant Interactions - II

We continue the discussion of our previous paper on writing down gauge invariant interacting equations for a bosonic string using the loop variable approach. In the earlier paper the equations were written down in one higher dimension where the fields are massless. In this paper we describe a procedure for dimensional reduction that gives interacting equations for fields with the same spectrum as in bosonic string theory. We also argue that the on-shell scattering amplitudes implied by these equations for the physical modes are the same as for the bosonic string. We check this explicitly for some of the simpler equations. The gauge transformation of space-time fields induced by gauge transformations of the loop variables are discussed in some detail. The unintegrated (i.e. before the Koba-Nielsen integration), regularized version of the equations, are gauge invariant off-shell (i.e. off the {\em free} mass shell).

hep-th↗
arXiv2000

Loop Variables and Gauge Invariant Interactions - I

We describe a method of writing down interacting equations for all the modes of the bosonic open string. It is a generalization of the loop variable approach that was used earlier for the free, and lowest order interacting cases. The generalization involves, as before, the introduction of a parameter to label the different strings involved in an interaction. The interacting string has thus becomes a ``band'' of finite width. The interaction equations expressed in terms of loop variables, has a simple invariance that is exact even off shell. A consistent definition of space-time fields requires the fields to be functions of all the infinite number of gauge coordinates (in addition to space time coordinates). The theory is formulated in one higher dimension, where the modes appear massless. The dimensional reduction that is needed to make contact with string theory (which has been discussed earlier for the free case) is not discussed here.

hep-th↗
arXiv1999

On the Role of Chaos in the AdS/CFT Connection

The question of how infalling matter in a pure state forms a Schwarzschild black hole that appears to be at non-zero temperature is discussed in the context of the AdS/CFT connection. It is argued that the phenomenon of self-thermalization in non-linear (chaotic) systems can be invoked to explain how the boundary theory, initially at zero temperature self thermalizes and acquires a finite temperature. Yang-Mills theory is known to be chaotic (classically) and the imaginary part of the gluon self-energy (damping rate of the gluon plasma) is expected to give the Lyapunov exponent. We explain how the imaginary part would arise in the corresponding supergravity calculation due to absorption at the horizon of the black hole.

hep-th↗
arXiv1999

High Temperature Limit of the N= 2 Matrix Model

The high temperature limit of a system of two D-0 branes is investigated. The partition function can be expressed as a power series in $β$ (inverse temperature). The leading term in the high temperature expression of the partition function and effective potential is calculated exactly. Physical quantities like the mean square separation can also be exactly determined in the high temperature limit.

hep-th↗
arXiv1998

The Hagedorn Transition, Deconfinement and the AdS/CFT Correspondence

A connection between the Hagedorn transition in string theory and the deconfinement transition in (non-supersymmetric) Yang-Mills theory is made using the AdS/CFT correspondence. We modify the model of zero temperature QCD proposed by Witten by compactifying an additional space-time coordinate with supersymmetry breaking boundary conditions thus introducing a finite temperature in the boundary theory. There is a Hagedorn-like transition associated with winding modes around this coordinate, which signals a topology changing phase transition to a new AdS/Schwarzschild blackhole where this coordinate is the time coordinate. In the boundary gauge theory time like Wilson loops acquire an expectation value above this temperature.

hep-th↗
arXiv1998

The Hagedorn Transition and the Matrix Model for Strings

We use the Matrix formalism to investigate what happens to strings above the Hagedorn temperaure. We show that it is not a limiting temperature but a temperature at which the continuum string picture breaks down. We study a collection of $N$ D-0-branes arranged to form a string having $N$ units of light cone momentum. We find that at high temperatures the favoured phase is one where the string world sheet has disappeared and the low energy degrees of freedom consists of $N^2$ massless particles (``gluons''). The nature of the transition is very similar to the deconfinement transition in large-N Yang Mills theories.

hep-th↗
arXiv1998

Interaction of F- and D-strings in the Matrix Model

We study a configuration of a parallel F- (fundamental) and D- string in IIB string theory by considering its T-dual configuration in the matrix model description of M-theory. We show that certain non-perturbative features of string theory such as $O(e^{-\frac{1}{g_{s}}})$ effects due to soliton loops, the existence of bound state (1,1) strings and manifest S-duality, can be seen in matrix models. We discuss certain subtleties that arise in the large-N limit when membranes are wrapped around compact dimensions.

hep-th↗
arXiv1997

Loop Variables and Gauge Invariant Interactions in String Theory

We describe a method of writing down the exact interacting gauge invariant equations for all the modes of the bosonic open string. It is a generalization of the loop variable approach that was used earlier for the free, and lowest order interacting cases. The generalization involves, as before, the introduction of a parameter to label the different strings involved in an interaction. The interacting string has thus becomes a ``band'' of finite width. As in the free case, the fields appear to be massless in one higher dimension. Although a proof of the consistency and gauge invariance to all orders (and thus of equivalence with string theory) is not yet available, plausibility arguments are given. We also give some simple illustrations of the procedure.

hep-th↗
arXiv1997

Fundamental Strings and D-strings in the IIB Matrix Model

The matrix model for IIB Superstring proposed by Ishibashi, Kawai, Kitazawa and Tsuchiya is investigated. Consideration of planar and non-planar diagrams suggests that the large N perturbative expansion is consistent with the double scaling limit proposed by the above authors. We write down a Wilson loop that can be interpreted as a fundamental string vertex operator. The one point tadpole in the presence of a D-string has the right form and this can be viewed as a matrix model derivation of the boundary conditions that define a D-string. We also argue that if world sheet coordinates $σ$ and $τ$ are introduced for the fundamental string, then the conjugate variable ${d}/{dσ}$ and ${d}/{dτ}$ can be interpreted as the D-string world sheet coordinates. In this way the $SL(2Z)$ duality group of the IIB superstring becomes identified with the symplectic group acting on ($p,q$).

hep-th↗