arXiv subjects

Vipul Periwal

Publications and source records attributed to Vipul Periwal.

At least 37 records · Page 2Linked to original sources

arXiv2000

Deformation quantization as the origin of D-brane non-Abelian degrees of freedom

I construct a map from the Grothendieck group of coherent sheaves to $K$-homology. This results in explicit realizations of $K$-homology cycles associated with D-brane configurations. Non-Abelian degrees of freedom arise in this framework from the deformation quantization of $N$-tuple cycles. The large $N$ limit of the gauge theory on D-branes wrapped on a subvariety $V$ of some variety $X$ is geometrically interpreted as the deformation quantization of the formal completion of $X$ along $V.$

hep-th↗

arXiv2000

D-brane charges and K-homology

It is argued that D-brane charge takes values in K-homology. For smooth manifolds with spin structure, this could explain why the phase factor $Ω(x)$ calculated with a D-brane state x in IIB theory appears in Diaconescu, Moore and Witten's computation of the partition function of IIA string theory.

hep-th↗

arXiv2000

Nonperturbative effects in deformation quantization

The Cattaneo-Felder path integral form of the perturbative Kontsevich deformation quantization formula is used to explicitly demonstrate the existence of nonperturbative corrections to na\"ıve deformation quantization.

hep-th↗

arXiv2000

Schwinger-Dyson = Wheeler-DeWitt: gauge theory observables as bulk operators

We argue that the second-order gauge-invariant Schwinger-Dyson operator of a gauge theory is the Wheeler-DeWitt operator in the dual string theory. Using this identification, we construct a set of operators in the gauge theory that correspond to excitations of gravity in the bulk. We show that these gauge theory operators have the expected properties for describing the semiclassical local gravity theory.

hep-th↗

arXiv1999

Dynamical truncation of the string spectrum at finite N

We exhibit a nonperturbative background independent dynamical truncation of the string spectrum and a quantization of the string coupling constant directly from the Hamiltonian governing the dynamics of strings constructed from Yang-Mills theories.

hep-th↗

arXiv1999

A toy model of Polyakov duality

Polyakov has conjectured that Yang-Mills theory should be equivalent to a noncritical string theory. I pointed out, based on the work of Marchesini, Ishibashi, Kawai and collaborators, and Jevicki and Rodrigues, that the loop operator of the Yang-Mills theory is the temporal gauge string field theory Hamiltonian of a noncritical string theory. In the present note I explicitly show how this works for the one--plaquette model, providing a consistent direct string interpretation of the unitary matrix model for the first time.

hep-th↗

arXiv1999

Dbrane Phase Transitions and Monodromy in K-theory

Majumder and Sen have given an explicit construction of a first order phase transition in a non-supersymmetric system of Dbranes that occurs when the B field is varied. We show that the description of this transition in terms of K-theory involves a bundle of K groups of non-commutative algebras over the Kahler cone with nontrivial monodromy. Thus the study of monodromy in K groups associated with quantized algebras can be used to predict the phase structure of systems of (non-supersymmetric) Dbranes.

hep-th↗

arXiv1999

String field theory Hamiltonians from Yang-Mills theories

Marchesini showed that the Fokker-Planck Hamiltonian for Yang-Mills theories is the loop operator. Jevicki and Rodrigues showed that the Fokker-Planck Hamiltonian of some matrix models co\"ıncides with temporal gauge non-critical string field theory Hamiltonians constructed by Ishibashi and Kawai (and their collaborators). Thus the loop operator for Yang-Mills theory is the temporal gauge Hamiltonian for a noncritical string field theory, in accord with Polyakov's conjecture. The consistency condition of the string interpretation is the zigzag symmetry emphasized by Polyakov. Several aspects of the noncritical string theory are considered, relating the string field theory Hamiltonian to the worldsheet description.

hep-th↗

arXiv1999

Cosmological and astrophysical tests of quantum gravity

Physics in the vicinity of an ultraviolet stable fixed point of a quantum field theory is parametrized by a renormalization group invariant macroscopic length scale, the correlation length $ξ,$ with the quantum effective action a function of this length scale. Numerical simulations of quantum gravity suggest the existence of just such a fixed point. Since the quantum effective action is a function only of $ξ,$ the cosmological constant must be $k ξ^{-2}$ with $k$ a pure number. Higher derivative terms are also parametrized by this length scale, so in particular the effective Newtonian dynamics of a test particle is modified at acceleration scales of order $1/ξ.$ Thus, renormalization group effects in quantum gravity provide a natural link between the phenomenological acceleration scale associated with galactic rotation curves and the value of the cosmological constant favoured by recent supernovae observations.

astro-ph↗

arXiv1999

A finite cutoff on the string worldsheet?

D-brane backgrounds are specified in closed string theories by holes with appropriate mixed Dirichlet and Neumann boundary conditions on the string worldsheet. As presently stated, the prescription defining D-brane backgrounds is such that the Einstein equation is not equivalent to the condition for scale invariance on the string worldsheet. A modified D-brane prescription is found, that leads to the desired equivalence, while preserving all known D-brane lore. A possible interpretation is that the worldsheet cutoff is finite. Possible connections to recent work of Maldacena and Strominger, and Gopakumar and Vafa are suggested.

hep-th↗

arXiv1999

The charge radius of a Dpbrane

Sen has shown that tachyon condensation in Dbrane-anti-Dbrane configurations can lead to remarkable connections between string theories. A consequence of his results is that there is a minimal value of the radial coordinate $r_{c} \propto \sqrt{α'} (gN)^{1/(9-p)}$ such that N units of D$p$brane charge cannot be localized to values smaller than $r_{c}.$ At this value of $r_{c}$ the curvature and the gradient of the Ramond-Ramond field strength are of order $1/α',$ and the vacuum, regarded as a Dbrane-anti-Dbrane configuration with a tachyon condensate, is rendered unstable, leading to a separation of the Dbrane and the anti-Dbrane. This value of $r_{c}$ lies in the region intermediate between the near-horizon regime and the asymptotic regime for Dbrane classical solutions for small $g$. This vacuum stability bound on the curvature can be interpreted as an uncertainty relation for Dbrane charge.

hep-th↗

arXiv1998

Dbrane boundstate wavefunctions

A simple WKB approximation gives explicit information about D0brane boundstate wavefunctions, suggesting that at large $N$ each individual D0brane has a wavefunction $\exp(- c r^{9/2}N^{-1/2}).$ Thus the velocity dependent interaction energy $v^{4}r^{-7}$ leads to an effective confining potential that grows as $r^{7}.$

hep-th↗

arXiv1998

Monopole condensates in SU(N) Yang-Mills Theory

Faddeev and Niemi have proposed a reformulation of SU(2) Yang-Mills theory in terms of new variables, appropriate for describing the theory in its infrared limit based on the intuitive picture of colour confinement due to monopole condensation. I generalize their proposal (with some differences) to SU(N) Yang-Mills theory. The natural variables are $N-1$ mutually commuting traceless $N\times N$ Hermitian matrices, an element of the maximal torus defined by these commuting matrices, $N-1$ Abelian gauge fields for the maximal torus gauge group, and an invariant symmetric two-index tensor on the tangent space of the maximal torus, adding up to the requisite 2$(N^{2}-1)$ physical degrees of freedom.

hep-th↗

arXiv1998

Functional statistical inference of parton distributions

Bialek, Callan and Strong have recently given a solution of the problem of determining a continuous probability distribution from a finite set of experimental measurements by formulating it as a one-dimensional quantum field theory. This report applies an extension of their formalism to the inference of functional parton distributions from scattering data.

hep-ph↗

arXiv1998

The topology of events

A matrix model is constructed to compute characteristic numbers of the space of subsets of $R^d $ with $N$ elements. This matrix model is found to be a constrained null dimensional reduction to a point of a Yang-Mills theory with anticommuting matter in $d+2$ dimensions. The constraints and equations of motion are similar to those found by Nishino and Sezgin in their 10+2 dimensional supersymmetric Yang-Mills equations. It is conjectured that the $d=10$ topological model is a twisted form of the Nishino-Sezgin model, dimensionally reduced to a point, due to SO(8) triality. Topological matrix models are constructed for non-commutative spaces, entirely in terms of algebras associated with such spaces. These models exhibit degrees of freedom analogous to massive modes in string theory.

hep-th↗

arXiv1998

Matrix string interactions

String configurations have been identified in compactified Matrix theory at vanishing string coupling. We show how the interactions of these strings are determined by the Yang-Mills gauge field on the worldsheet. At finite string coupling, this suggests the underlying dynamics is not well-approximated as a theory of strings. This may explain why string perturbation theory diverges badly, while Matrix string perturbation theory presumably has a perturbative expansion with properties similar to the strong coupling expansion of 2d Yang-Mills theory.

hep-th↗

arXiv1998

Flow of low energy couplings in the Wilson renormalization group

A new form of the Wilson renormalization group equation is derived, in which the flow equations are, up to linear terms, proportional to a gradient flow. A set of coördinates is found in which the flow of marginal, low-energy, couplings takes a gradient form, if relevant couplings are tuned to vanish.

hep-th↗

arXiv1998

Consistency of Wilsonian effective actions

Wilsonian effective actions are interpreted as free energies in ensembles with prescribed field expectation values and prescribed connected two-point functions. Since such free energies are directly obtained from two-particle-irreducible functionals, it follows that Wilsonian effective actions satisfy elementary perturbative consistency conditions, and non-perturbative convexity conditions. In particular, the exact determination of a Wilsonian action by other means (e.g. supersymmetry) allows one to extract restrictions on the particular cutoff scheme and field reparametrization that would lead to such a Wilsonian action from an underlying microscopic action.

hep-th↗