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Romuald A. Janik

Publications and source records attributed to Romuald A. Janik.

At least 91 records · Page 5Linked to original sources
arXiv2004

Quantum rolling tachyon

We consider the quantum treatment of the rolling tachyon background describing the decay of D-branes in the limit of weak string coupling. We focus on the propagation of an open string in the fluctuating background and show how the boundary string action is modified by quantum effects. A bilocal term in the boundary action is generated which, however, does not spoil the vanishing of the $β$ function at one loop. The propagation of an open string for large times is found to be very strongly suppressed.

hep-th↗
arXiv2003

Multiplying unitary random matrices - universality and spectral properties

In this paper we calculate, in the large N limit, the eigenvalue density of an infinite product of random unitary matrices, each of them generated by a random hermitian matrix. This is equivalent to solving unitary diffusion generated by a hamiltonian random in time. We find that the result is universal and depends only on the second moment of the generator of the stochastic evolution. We find indications of critical behavior (eigenvalue spacing scaling like $1/N^{3/4}$) close to $θ=π$ for a specific critical evolution time $t_c$.

math-ph↗
arXiv2003

The decay of quantum D-branes

We study the {\em quantum} decay of D0-branes in two-dimensional 0B string theory. The quantum nature of the branes provides a natural cut-off for the closed string emission rate. We find exact quantum mechanical wavefunctions for the decaying branes and show how one can include the effects of the Fermi sea for any string coupling (Fermi energy).

hep-th↗
arXiv2003

Exact U(N_c)-> U(N_1)xU(N_2) factorization of Seiberg-Witten curves and N=1 vacua

N=2 gauge theories broken down to N=1 by a tree level superpotential are necessarily at the points in the moduli space where the Seiberg-Witten curve factorizes. We find exact solution to the factorization problem of Seiberg-Witten curves associated with the breaking of the U(N_c) gauge group down to two factors U(N_1)xU(N_2). The result is a function of three discrete parameters and two continuous ones. We find discrete identifications between various sets of parameters and comment on their relation to the global structure of N=1 vacua and their various possible dual descriptions. In an appendix we show directly that integrality of periods leads to factorization.

hep-th↗
arXiv2003

The Lund Model at Nonzero Impact Parameter

We extend the formulation of the longitudinal 1+1 dimensional Lund model to nonzero impact parameter using the minimal area assumption. Complete formulae for the string breaking probability and the momenta of the produced mesons are derived using the string worldsheet Minkowskian helicoid geometry. For strings stretched into the transverse dimension, we find probability distribution with slope linear in m_T similar to the statistical models but without any thermalization assumptions.

hep-ph↗
arXiv2003

Infinite Products of Large Random Matrices and Matrix-valued Diffusion

We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a natural matrix-valued multiplicative diffusion process. In both cases of hermitian and complex matrices, we observe an emergence of "topological phase transition" in the spectrum, after some critical diffusion time $τ_{\rm crit}$ is reached. In the case of the particular product of two hermitian ensembles, we observe also an unusual localization-delocalization phase transition in the spectrum of the considered ensemble. We verify the analytical formulae obtained in this work by numerical simulation.

math-ph↗
arXiv2003

Effective matter superpotentials from Wishart random matrices

We show how within the Dijkgraaf-Vafa prescription one can derive superpotentials for matter fields. The ingredients forming the non-perturbative Affleck-Dine-Seiberg superpotentials arise from constrained matrix integrals, which are equivalent to classical complex Wishart random matrices. The mechanism is similar to the way the Veneziano-Yankielowicz superpotential arises from the matrix model measure.

hep-th↗
arXiv2003

Explicit factorization of Seiberg-Witten curves with matter from random matrix models

Within the Dijkgraaf-Vafa correspondence, we study the complete factorization of the Seiberg-Witten curve for U(N_c) gauge theory with N_f<N_c massive flavors. We obtain explicit expressions, from random matrix theory, for the moduli, parametrizing the curve. These moduli characterize the submanifold of the Coulomb branch where all monopoles become massless. We find that the matrix model reveals some non-trivial structures of the gauge theory. In particular the moduli are additive with respect to adding extra matter and increasing the number of colors.

hep-th↗
arXiv2003

The Dijkgraaf-Vafa correspondence for theories with fundamental matter fields

In this talk I describe some applications of random matrix models to the study of N=1 supersymmetric Yang-Mills theories with matter fields in the fundamental representation. I review the derivation of the Veneziano-Yankielowicz-Taylor/Affleck-Dine-Seiberg superpotentials from constrained random matrix models (hep-th/0211082), a field theoretical justification of the logarithmic matter contribution to the Veneziano-Yankielowicz-Taylor superpotential (hep-th/0306242) and the random matrix based solution of the complete factorization problem of Seiberg-Witten curves for N=2 theories with fundamental matter (hep-th/0212212).

hep-th↗
arXiv2003

Backreaction and the rolling tachyon -- an effective action point of view

We compute the decay of an unstable D9 brane in type IIA string theory including backreaction effects using an effective field theory approach. The open string tachyon on the brane is coupled consistently to the space-time metric, the dilaton and the RR 9-form. The purpose of this note is to address the fate of the open string energy density, which remains constant if no interaction with the closed string modes is included. Our computations show that taking only into account the coupling to the massless closed strings the total energy stored in the open string sector vanishes asymptotically, independently how small one chooses g_s. We find also the large time behaviour of the fields in the Einstein and string frames.

hep-th↗
arXiv2002

Wishart and Anti-Wishart random matrices

We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices $A^\dagger A$, for any finite number of rows and columns of $A$, without any large N approximations. In particular we treat the case when the Wishart-type random matrix contains redundant, non-random information, which is a new result. This representation is of interest for a procedure of reconstructing the redundant information hidden in Wishart matrices, with potential applications to numerous models based on biological, social and artificial intelligence networks.

math-ph↗
arXiv2002

BMN operators and string field theory

We extract from gauge theoretical calculations the matrix elements of the SYM dilatation operator. By the BMN correspondence this should coincide with the 3-string vertex of light cone string field theory in the pp-wave background. We find a mild but important discrepancy with the SFT results. If the modified $O(g_2)$ matrix elements are used, the $O(g_2^2)$ anomalous dimensions are exactly reproduced without the need for a contact interaction in the single string sector.

hep-th↗
arXiv2002

QCD, diffraction and string theory

Recently, string theory on some specific curved backgroud spacetime geometries has been conjectured to be equivalent to certain gauge theories (AdS/CFT correspondence). This correspondence may be used to investigate the non-perturbative regime of gauge theories. I describe its application to the study of soft scattering amplitudes in a confining gauge theory. I describe two qualitatively different applications: amplitudes with vacuum quantum number exchange (Pomeron-like), amplitudes with Reggeon exchange. The last case requires going beyond eikonal approximation on the gauge theory side.

hep-ph↗
arXiv2002

Prompt Multi-Gluon Production in High Energy Collisions from Singular Yang-Mills Solutions

We study non-perturbative parton-parton scattering in the Landau method using singular O(3) symmetric solutions to the Euclidean Yang-Mills equations. These solutions combine instanton dynamics (tunneling) and overlap (transition) between incoming and vacuum fields. We derive a high-energy solution at small Euclidean times, and assess its susequent escape and decay into gluons in Minkowski space-time. We describe the spectrum of the {\it outgoing} gluons and show that it is related through a particular rescaling to the Yang-Mills sphaleron explosion studied earlier. We assess the number of {\it incoming} gluons in the same configuration, and argue that the observed scaling is in fact more general and describes the energy dependence of the spectra and multiplicities at {\it all} energies. Applications to hadron-hadron and nucleus-nucleus collisions are discussed elsewhere.

hep-ph↗
arXiv2002

New Multicritical Random Matrix Ensembles

In this paper we construct a class of random matrix ensembles labelled by a real parameter $α\in (0,1)$, whose eigenvalue density near zero behaves like $|x|^α$. The eigenvalue spacing near zero scales like $1/N^{1/(1+α)}$ and thus these ensembles are representatives of a {\em continous} series of new universality classes. We study these ensembles both in the bulk and on the scale of eigenvalue spacing. In the former case we obtain formulas for the eigenvalue density, while in the latter case we obtain approximate expressions for the scaling functions in the microscopic limit using a very simple approximate method based on the location of zeroes of orthogonal polynomials.

hep-th↗
arXiv2001

High energy scattering and AdS/CFT

In this talk we describe the application of the AdS/CFT correspondence for a confining background to the study of high energy scattering amplitudes in gauge theory. We relate the energy behaviour of scattering amplitudes to properties of minimal surfaces of the helicoidal type. We describe the results of hep-th/0003059 and hep-th/0010069 for amplitudes with vacuum quantum number exchange and, very briefly, hep-th/0110024 on the extension of this formalism to Reggeon exchange.

hep-th↗
arXiv2001

Exceptional boundary states at c=1

We consider the CFT of a free boson compactified on a circle, such that the compactification radius $R$ is an irrational multiple of $R_{selfdual}$. Apart from the standard Dirichlet and Neumann boundary states, Friedan suggested [1] that an additional 1-parameter family of boundary states exists. These states break U(1) symmetry of the theory, but still preserve conformal invariance. In this paper we give an explicit construction of these states, show that they are uniquely determined by the Cardy-Lewellen sewing constraints, and we study the spectrum in the `open string channel', which is given here by a continous integral with a nonnegative measure on the space of conformal weights.

hep-th↗