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Shyamoli Chaudhuri

Publications and source records attributed to Shyamoli Chaudhuri.

At least 19 recordsLinked to original sources
arXiv2018

Heterotic Type I Strings at High Temperature

We show that the high temperature limits of the heterotic E8xE8 and Spin(32)/Z2 strings and their Type I A/B superstring duals are finite and convergent. The Hagedorn growth of the degeneracies in the string mass level expansion is suppressed by an exponential linear in the mass level number for both heterotic strings, and suppressed by the exponential of the negative square root of the mass level number for the Type IB superstring. However, in the massless gauge field theoretic limit of the Type IB open and closed superstring, we find clear evidence for the thermal deconfinement phase transition at the self-dual temperature by examining the annulus graph alone. Above the self-dual temperature, there is a discontinuity in the first derivative with respect to temperature of both the free energy, and the heavy quark potential, leading to a deconfined thermal gluon ensemble, with universal 1/r potential, and temperature dependent corrections, as predicted by Luscher and Weisz. A number of essential aspects of the worldsheet formalism of the heterotic strings are derived in an appendix, deducing thereby the O8-D0-D8brane Type IA duals of all of the heterotic CHL island universe moduli spaces.

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arXiv2018

Euclidean Time Formulation for the Superstring Ensembles: Perturbative Canonical Ensemble with Neveu-Schwarz B Field Backgrounds

The lengthy discussion and derivations given in this paper have been corrected, and completed with additional results and greater simplicity. We show that the high temperature limits of the heterotic E8xE8 and Spin(32)/Z2 strings and their Type I A/B superstring duals are finite and convergent. The Hagedorn growth of the degeneracies in the string mass level expansion is suppressed by an exponential linear in the mass level number for both heterotic strings, and suppressed by the exponential of the negative square root of the mass level number for the Type IB superstring. However, in the massless gauge field theoretic limit of the Type IB open and closed superstring, we find clear evidence for the thermal deconfinement phase transition at the self-dual temperature by examining the annulus graph alone. Above the self-dual temperature, there is a discontinuity in the first derivative with respect to temperature of both the free energy, and the heavy quark potential, leading to a deconfined thermal gluon ensemble, with universal 1/r potential, and temperature dependent corrections, as predicted by Luscher and Weisz. A number of essential aspects of the worldsheet formalism of the heterotic strings are derived in an appendix, deducing thereby the O8-D0-D8brane Type IA duals of all of the heterotic CHL island universe moduli spaces.

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arXiv2005

Thermal Duality and the String Canonical Ensemble

We derive the free energies of both the closed heterotic, and the unoriented, open and closed, type I string ensembles, consistent with the thermal (Euclidean T-duality) transformations on the String/M Duality Web. A crucial role is played by a temperature dependent Wilson line wrapping Euclidean time, responsible for the spontaneous breaking of supersymmetry at finite temperature while eliminating thermal tachyons, and determined uniquely by thermal duality. Conversely, we can show that the absence of a Yang-Mills gauge sector precludes the possibility of an equilibrium type II canonical ensemble prior to the introduction of background Dbranes or fluxes. As a consistency check, we verify that our results for the string free energy always reproduce the T^{10} growth expected in the low energy field theory limits while displaying a dramatically slower T^2 growth at temperatures above the string scale. We present both the low and high temperature expansions for the one-loop heterotic and type I string free energies, results which follow from an explicit term-by-term evaluation of the modular integrals in the string mass level expansion.

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arXiv2005

Finite Temperature Closed Superstring Theory

We find that the gas of IIA strings undergoes a phase transition into a gas of IIB strings at the self-dual temperature. A gas of free heterotic strings undergoes a Kosterlitz-Thouless duality transition with positive free energy and positive specific heat but vanishing internal energy at criticality. We examine the consequences of requiring a tachyon-free thermal string spectrum. We show that in the absence of Ramond-Ramond fluxes the IIA and IIB string ensembles are thermodynamically ill-defined. The 10D heterotic superstrings have nonabelian gauge fields and in the presence of a temperature dependent Wilson line background are found to share a stable and tachyon-free ground state at all temperatures starting from zero with gauge group SO(16)xSO(16). The internal energy of the heterotic string is a monotonically increasing function of temperature with a stable and supersymmetric zero temperature limit. Our results point to the necessity of gauge fields in a viable weakly coupled superstring theory. Note Added (Sep 2005).

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arXiv2005

Finite Temperature Gases of Fermionic Strings

We show that in the absence of a Ramond-Ramond sector both the type IIA and type IIB free string gases have a thermal instability due to low temperature tachyon modes. The gas of free IIA strings undergoes a thermal duality transition into a gas of free IIB strings at the self-dual temperature. The free heterotic string gas is a tachyon-free ensemble with gauge symmetry SO(16)$\times$SO(16) in the presence of a timelike Wilson line background. It exhibits a holographic duality relation undergoing a self-dual phase transition with positive free energy and positive specific heat. The type IB open and closed string ensemble is related by thermal duality to the type I' string ensemble. We identify the order parameter for the Kosterlitz-Thouless phase transition from a low temperature gas of short open strings to a high temperature long string phase at or below T_C. Note Added (Sep 2005).

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arXiv2005

Thermal Tachyons and the "g"-Theorem

We give a pedagogical introduction to Affleck and Ludwig's g-theorem, distinguishing its applications in field theory vs string theory. We clarify the recent proposal that the vacuum degeneracy $g$ of a noncompact worldsheet sigma model with a continuous spectrum of scaling dimensions is lowered under renormalization group flow while preserving the central charge. As an illustration we argue that the IR stable endpoint of the relevant flow of the worldsheet RG induced by a thermal tachyon in the type II string is the noncompact supersymmetric vacuum with lower $g$. Note Added (Sep 2005).

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arXiv2005

Holography and the Canonical Ensemble of Fermionic Strings

We show that the canonical ensemble in any of the six supersymmetric string theories, type IIA and IIB, type IB and type I', or heterotic E_8 x E_8 and Spin(32)/Z_2, exhibits a strong version of holography: the growth of the number of degrees of freedom in the free energy at high temperatures is identical to that in a two-dimensional quantum field theory. We clarify the precise nature of the thermal duality phase transition in each case, confirming that it lies within the Kosterlitz-Thouless universality class. We show that, in the presence of Dbranes, and a consequent Yang-Mills gauge sector, the thermal ensemble of type II strings is infrared stable, with neither tachyons nor massless scalar tadpoles. Supersymmetry remains unbroken in the oriented closed string sector, but is broken by thermal effects in the full unoriented open and closed type I string theory. We identify an order parameter for an unusual phase transition in the worldvolume gauge theory signalled by the short distance behavior of the pair correlator of timelike Wilson loops. Note Added (Sep 2005).

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arXiv2005

Duality Phase Transition in Type I String Theory

We show that the duality phase transition in the unoriented type I theory of open and closed strings is_first order_. The order parameter is the semiclassical approximation to the heavy quark-antiquark potential at finite temperature, extracted from the covariant off-shell string amplitude with Wilson loop boundaries wrapped around the Euclidean time direction. Remarkably, precise calculations can be carried out on either side of the phase boundary at the string scale T_C = 1/2πα^{'1/2} by utilizing the T-dual, type IB and type I', descriptions of the short string gas of massless gluon radiation. We will calculate the change in the duality transition temperature in the presence of an electromagnetic background field.

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arXiv2005

Thermal Duality Transformations and the Canonical Ensemble: The Deconfining Long String Phase Transition

We give a first principles formulation of the equilibrium statistical mechanics of strings in the canonical ensemble, compatible with the Euclidean timelike T-duality transformations that link the six supersymmetric string theories in pairs. We demonstrate that each exhibits a T^2 growth in the free energy at high temperatures far above the string scale. We verify that the low energy field theory limit of our expression for the string free energy reproduces the expected T^{10} growth when the contribution from massive string modes is suppressed. In every case, heterotic, type I, and type II, we can definitively rule out the occurrence of an exponential divergence in the one-loop string free energy above some critical temperature. Finally, we identify a macroscopic loop amplitude in the type I string theories which yields the expectation value of a single Wilson-Polyakov-Susskind loop in the low energy finite temperature supersymmetric gauge theory limit, an order parameter for a thermal phase transition at a string scale temperature. We point out that precise computations can nevertheless be carried out on either side of the phase boundary by using the low energy finite temperature supersymmetric gauge theory limits of the pair of thermal dual string theories, type IB and type I'. Note Added (Sep 2005).

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arXiv2005

Electric-Magnetic Duality, Matrices, & Emergent Spacetime

This is a rough transcript of talks given at the Workshop on Groups & Algebras in M Theory at Rutgers University, May 31--Jun 04, 2005. We review the basic motivation for a pre-geometric formulation of nonperturbative String/M theory, and for an underlying eleven-dimensional electric-magnetic duality, based on our current understanding of the String/M Duality Web. We explain the concept of an emerging spacetime geometry in the large N limit of a U(N) flavor matrix Lagrangian, distinguishing our proposal from generic proposals for quantum geometry, and explaining why it can incorporate curved spacetime backgrounds. We assess the significance of the extended symmetry algebra of the matrix Lagrangian, raising the question of whether our goal should be a duality covariant, or merely duality invariant, Lagrangian. We explain the conjectured isomorphism between the O(1/N) corrections in any given large N scaling limit of the matrix Lagrangian, and the corresponding alpha' corrections in a string effective Lagrangian describing some weak-coupling limit of the String/M Duality Web.

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arXiv2005

CHL Compactifications and Beyond

This is the transcript of a talk given at the 3rd Simons Workshop in Mathematics and Physics on July 26, 2005. We review the genesis of the CHL (Chaudhuri-Hockney-Lykken) project, explaining both its phenomenological goals and theoretical justification in light of the known vast proliferation of N=1 string vacua. We explain what a CHL compactification is, review some key results such as the construction of moduli spaces with a small number of massless scalar fields, the decompactification of such moduli spaces to one of five consistent ten-dimensional superstring theories, and the appearance of electric-magnetic duality in only the four-dimensional moduli spaces, a 1995 observation due to Chaudhuri & Polchinski.

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arXiv2005

CHL Compactifications Revisited

CHL compactifications are supersymmetry preserving orbifolds of any perturbatively renormalizable and ultraviolet finite ground state of the perturbative string theories: heterotic, type I, or type II, preserving 32, 16, 12, 8, 4, (or zero) supersymmetries, and retaining the perturbative renormalizability and finiteness of the parent string vacuum. In this paper, we review the genesis of the CHL (Chaudhuri-Hockney-Lykken) project within the broader context of the full String/M Duality web, establishing the existence of moduli spaces with a small number of massless scalar fields, the decompactification of such moduli spaces to one of the five ten-dimensional superstring theories, and the appearance of electric-magnetic duality in only the four-dimensional moduli spaces, a 1995 observation due to Chaudhuri & Polchinski. We present two mathematical curiosities easily deduced from the fermionic current algebra representation but whose physical significance is a puzzle: a 4D N=4 heterotic string vacuum with no massless scalar fields other than the dilaton, and a 2D N=8 heterotic string vacuum with no abelian gauge fields, reiterating once more the necessity for a systematic classification of the CHL orbifolds.

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arXiv2005

Nonperturbative Type I-I' String Theory

We propose a nonperturbative framework for the O(32) type I open and closed string theory. The short distance degrees of freedom are bosonic and fermionic hermitian matrices belonging respectively to the adjoint and fundamental representations of the special unitary group SU(N). We identify a closed matrix algebra at finite N which corresponds to the Lorentz, gauge, and supersymmetry algebras of the large N continuum limit. The planar reduction of our matrix theory coincides with the low energy spacetime effective action of the d=10 type I O(32) unoriented open and closed string theory. We show that matrix T-duality transformations can yield a nonperturbative framework for the T-dual type I' closed string theory with 32 D8branes. We show further that under a strong-weak coupling duality transformation the large N reduced action coincides with the low energy spacetime effective action of the d=10 heterotic string, an equivalence at leading order in the inverse string tension and with either gauge group Spin(32)/Z2 or E8xE8. Our matrix formalism has the potential of providing a nonperturbative framework encapsulating all of the weak coupling limits of M theory.

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arXiv2005

Spontaneous Breaking of Diffeomorphism Invariance in Matrix Theory

We present a matrix action based on the unitary group U(N) whose large N ground states are conjectured to be in precise correspondence with the weak-strong dual effective field theory limits of M theory preserving sixteen supersymmetries. We identify a finite N matrix algebra that corresponds to the spacetime and internal symmetry algebra of the Lorentz invariant field theories obtained in the different large N limits. The manifest diffeomorphism invariance of matrix theory is spontaneously broken upon specification of the large N ground state. We verify that there exist planar limits which yield the low energy spacetime effective actions of all six supersymmetric string theories in nine spacetime dimensions and with sixteen supercharges.

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arXiv2005

Bosonic Matrix Theory and Matrix Dbranes

We develop new tools for an in-depth study of our recent proposal for Matrix Theory. We construct the anomaly-free and finite planar continuum limit of the ground state with SO(2^{13}) symmetry matching with the tadpole and tachyon free IR stable high temperature ground state of the open and closed bosonic string. The correspondence between large N limits and spacetime effective actions is demonstrated more generally for an arbitrary D25brane ground state which might include brane-antibrane pairs or NS-branes and which need not have an action formulation. Closure of the finite N matrix Lorentz algebra nevertheless requires that such a ground state is simultaneously charged under all even rank antisymmetric matrix potentials. Additional invariance under the gauge symmetry mediated by the one-form matrix potential requires a ground state charged under the full spectrum of antisymmetric (p+1)-form matrix potentials with p taking any integer value less than 26. Matrix Dbrane democracy has a beautiful large N remnant in the form of mixed Chern-Simons couplings in the effective Lagrangian whenever the one-form gauge symmetry is nonabelian.

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arXiv2005

A New Proposal for Matrix Theory

We explain the motivation and main ideas underlying our proposal for a Lagrangian for Matrix Theory based on sixteen supercharges. Starting with the pedagogical example of a bosonic matrix theory we describe the appearance of a continuum spacetime geometry from a discrete, and noncommutative, spacetime with both Lorentz and Yang-Mills invariances. We explain the appearance of large N ground states with Dbranes and elucidate the principle of matrix Dbrane democracy at finite N. Based on the underlying symmetry algebras that hold at both finite and infinite N, we show why the supersymmetric matrix Lagrangian we propose does not belong to the class of supermatrix models which includes the BFSS and IKKT Matrix Models. We end with a preliminary discussion of a path integral prescription for the Hartle-Hawking wavefunction of the Universe derived from Matrix Theory.

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arXiv2005

11d Electric-Magnetic Duality and the Dbrane Spectrum

We consider the gedanken calculation of the pair correlation function of spatially-separated macroscopic string solitons in strongly coupled type IIA string/M theory, with the macroscopic strings wrapping the eleventh dimension. The supergravity limit of this correlation function with well-separated, pointlike macroscopic strings corresponds to having also taken the IIA string coupling constant to zero. Thus, the pointlike limit of the gedanken correlation function can be given a precise worldsheet description in the 10D weakly-coupled type IIA string theory, analysed by us in hep-th/0007056 [Nucl. Phys. B591 (2000) 243]. The requisite type IIA string amplitude is the supersymmetric extension of the worldsheet formulation of an off-shell closed string tree propagator in bosonic string theory, a 1986 analysis due to Cohen, Moore, Nelson, and Polchinski. We point out that the evidence for pointlike sources of the zero-form field strength provided by our worldsheet results clarifies that the electric-magnetic duality in the Dirichlet-brane spectrum of type II string theories is eleven-dimensional.

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