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#### Correlation functions and AdS/LCFT correspondence

, Article Nuclear Physics B ; Volume 696, Issue 3 , 2004 , Pages 492-502 ; 05503213 (ISSN) ; Rouhani, S ; Saadat, M ; Sharif University of Technology
2004

Abstract

Correlation functions of logarithmic conformal field theory is investigated using the ADS/CFT correspondence and a novel method based on nilpotent weights and 'superfields'. Adding an specific form of interaction, we introduce a perturbative method to calculate the correlation functions. © 2004 Elsevier B.V. All rights reserved

#### On the AdS/CFT correspondence and logarithmic operators

, Article Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics ; Volume 518, Issue 1-2 , 2001 , Pages 157-162 ; 03702693 (ISSN) ; Rouhani, S ; Saadat, M ; Sharif University of Technology
2001

Abstract

Logarithmic conformal field theory is investigated using the ADS/CFT correspondence and a novel method based on nilpotent weights. Using this device we add ghost fermions and point to a BRST invariance of the theory. © 2001 Elsevier Science B.V. All rights reserved

#### SLE(κ,ρ) and boundary Coulomb gas

, Article Nuclear Physics B ; Volume 740, Issue 3 , 2006 , Pages 348-357 ; 05503213 (ISSN) ; Rajabpour, M. A ; Rouhani, S ; Sharif University of Technology
2006

Abstract

We consider the Coulomb gas model on the upper half-plane with different boundary conditions, namely, Dirichlet, Neumann and mixed. We relate this model to SLE(κ, ρ) theories. We derive a set of conditions connecting the total charge of the Coulomb gas, the boundary charges, the parameters κ and ρ. Also we study a free fermion theory in presence of a boundary and show with the same methods that it would lead to logarithmic boundary changing operators. © Elsevier B.V. All rights reserved

#### Logarithmic conformal null vectors and SLE

, Article Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics ; Volume 600, Issue 3-4 , 2004 , Pages 297-301 ; 03702693 (ISSN) ; Rajabpour, M. A ; Rouhani, S ; Sharif University of Technology
2004

Abstract

Formal Loewner evolution is connected to conformal field theory. In this Letter we introduce an extension of Loewner evolution, which consists of two coupled equations and connect the martingales of these equations to the null vectors of logarithmic conformal field theory. © 2004 Elsevier B.V. All rights reserved

#### Current algebra associated with logarithmic conformal field theories

, Article Letters in Mathematical Physics ; Volume 55, Issue 1 , 2001 , Pages 71-76 ; 03779017 (ISSN) ; Rouhani, S ; Saadat, M ; Sharif University of Technology
2001

Abstract

We propose a general framework for deriving the OPEs within a logarithmic conformal field theory (LCFT). This naturally leads to the emergence of a logarithmetic partner of the energy momentum tensor within an LCFTand implies that the current algebra associated with an LCFT is expanded. We derive this algebra for a generic LCFTand discuss some of its implications. We observe that two constants arise in the OPE of the energy-momentum tensor with itself. One of these is the usual central charge

#### Logarithmic conformal field theories near a boundary

, Article Letters in Mathematical Physics ; Volume 53, Issue 1 , 2000 , Pages 49-57 ; 03779017 (ISSN) ; Rouhani, S ; Sharif University of Technology
Springer Netherlands
2000

Abstract

We consider logarithmic conformal field theories near a boundary and derive the general form of one and two point functions. We obtain results for arbitrary and two dimensions. Application to two-dimensional magnetohydrodynamics is discussed

#### "Volume-preserving" conformational rheological models for multi-component miscible polymer blends using the GENERIC formalism

, Article Macromolecular Theory and Simulations ; Volume 12, Issue 7 , 2003 , Pages 524-530 ; 10221344 (ISSN) ; Ramazani, A ; Khonakdar, H. A ; Sharif University of Technology
2003

Abstract

A family of conformational rheological models for multi-component miscible polymer blends is developed using a modified form of the Poisson bracket formulation. Two conformation tensors called c1 and c2 are introduced to show the orientation of the first and the second components of a blend, respectively. The mobility tensor and the energy function for each blend component are expressed in terms of these conformation tensors. The interaction effects are also included by energy expressions. The predictions of this family of "volume-preserving" models are illustrated for a Hookean-type energy function and several expressions of the modified mobility tensors. The results are illustrated for...

#### On the β-function and conformal anomaly of noncommutative QED with adjoint matter fields

, Article International Journal of Modern Physics A ; Volume 18, Issue 15 , 2003 , Pages 2591-2607 ; 0217751X (ISSN) ; Mohammadi, M ; Sharif University of Technology
2003

Abstract

In the first part of this work, a perturbative analysis up to one-loop order is carried out to determine the one-loop β-function of noncommutative U(1) gauge theory with matter fields in the adjoint representation. In the second part, the conformal anomaly of the same theory is calculated using Fujikawa's path integral method. The value of the one-loop β-function calculated in both methods coincides. As it turns out, noncommutative QED with matter fields in the adjoint representation is asymptotically free for the number of flavor degrees of freedom Nf < 3

#### Calculation of four-point correlation function of logarithmic conformal field theory using AdS/CFT correspondence

, Article Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics ; Volume 548, Issue 3-4 , 2002 , Pages 237-242 ; 03702693 (ISSN) ; Rouhani, S ; Sharif University of Technology
2002

Abstract

We use the correspondence between scalar field theory on AdS and induced conformal field theory on its boundary to calculate correlation functions of logarithmic conformal field theory in arbitrary dimensions. Our calculations utilize the newly proposed method of nilpotent weights. We derive expressions for the four point function assuming a generic interaction term. © 2002 Elsevier Science B.V. All rights reserved

#### Logarithmic conformal field theory through nilpotent conformal dimensions

, Article Nuclear Physics B ; Volume 599, Issue 3 , 2001 , Pages 531-546 ; 05503213 (ISSN) ; Rouhani, S ; Saadat, M ; Sharif University of Technology
2001

Abstract

We study logarithmic conformal field theories (LCFTs) through the introduction of nilpotent conformal weights. Using this device, we derive the properties of LCFTs such as the transformation laws, singular vectors and the structure of correlation functions. We discuss the emergence of an extra energy momentum tensor, which is the logarithmic partner of the energy momentum tensor. © 2001 Elsevier Science B.V

#### Disordered systems and logarithmic conformal field theory

, Article International Journal of Modern Physics A ; Volume 18, Issue 25 , 2003 , Pages 4703-4745 ; 0217751X (ISSN) ; Sharif University of Technology
2003

Abstract

We review a recent development in theoretical understanding of the quenched averaged correlation functions of disordered systems and the logarithmic conformal field theory (LCFT) in d-dimensions. The logarithmic conformal field theory is the generalization of the conformal field theory when the dilatation operator is not diagonal and has the Jordan form. It is discussed that at the random fixed point the disordered systems such as random-bond Ising model, Polymer chain, etc. are described by LCFT and their correlation functions have logarithmic singularities. As an example we discuss in detail the application of LCFT to the problem of random-bond Ising model in 2 ≤ d ≤ 4

#### Non-Relativistic Conformal Symmetries; Infinite Extensions and Logarithmic Representation

, Ph.D. Dissertation Sharif University of Technology ; Rouhani, Shahin (Supervisor)
Abstract

We study different aspects of non-relativistic conformal symmetries. Schrodinger and Galilean Conformal Algebra (GCA) are reviewed extensively. We as well study possible extensions of non-relativistic conformal symmetries. We find a new class of infinite dimensional non-relativistic conformal symmetries in 2+1. We study logarithmic representation of Schrodinger symmetry. As well we utilize contraction approach and obtain both ordinary and logarithmic representations of GCA. Finally we investigate some aspects of logarithmic GCA in the context of holography principle

#### Conformal upper bounds for the eigenvalues of the Laplacian and Steklov problem

, Article Journal of Functional Analysis ; Volume 261, Issue 12 , 2011 , Pages 3419-3436 ; 00221236 (ISSN) ; Sharif University of Technology
2011

Abstract

In this paper, we find upper bounds for the eigenvalues of the Laplacian in the conformal class of a compact Riemannian manifold (M,g). These upper bounds depend only on the dimension and a conformal invariant that we call "min-conformal volume". Asymptotically, these bounds are consistent with the Weyl law and improve previous results by Korevaar and Yang and Yau. The proof relies on the construction of a suitable family of disjoint domains providing supports for a family of test functions. This method is interesting for itself and powerful. As a further application of the method we obtain an upper bound for the eigenvalues of the Steklov problem in a domain with C1 boundary in a complete...

#### Perturbed logarithmic CFT and integrable models

, Article Nuclear Physics B ; Volume 754, Issue 3 , 2006 , Pages 283-292 ; 05503213 (ISSN) ; Rouhani, S ; Sharif University of Technology
2006

Abstract

Perturbation of logarithmic conformal field theories using Zamolodchikov's method is investigated. We derive conditions for the perturbing operator, such that the perturbed model be integrable. We also consider an example where an integrable model arises out of perturbation of the c = - 2 logarithmic conformal field theory. © 2006 Elsevier B.V. All rights reserved

#### Abelian sandpile model: A conformal field theory point of view

, Article Nuclear Physics B ; Volume 718, Issue 3 , 2005 , Pages 362-370 ; 05503213 (ISSN) ; Rajabpour, M. A ; Rouhani, S ; Sharif University of Technology
2005

Abstract

In this paper we derive the scaling fields in c = -2 conformal field theory associated with weakly allowed clusters in Abelian sandpile model and show a direct relation between the two models. © 2005 Elsevier B.V. All rights reserved

#### Watersheds are schramm-loewner evolution curves

, Article Physical Review Letters ; Volume 109, Issue 21 , 2012 ; 00319007 (ISSN) ; Araújo, N. A. M ; Schrenk, K. J ; Rouhani, S ; Herrmann, H. J ; Sharif University of Technology
2012

Abstract

We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner evolution (SLE) curves, being described by one single parameter κ. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLEκ, with κ=1.734±0.005, being the only known physical example of an SLE with κ<2. This lies outside the well-known duality conjecture, bringing up new questions regarding the existence and reversibility of dual models. Furthermore, it constitutes a strong indication for conformal invariance in random landscapes and suggests that watersheds likely correspond to a logarithmic conformal field theory with a central charge c-7/2

#### Conformation of repaglinide: a solvent dependent structure

, Article Journal of Molecular Structure ; Volume 1143 , 2017 , Pages 388-396 ; 00222860 (ISSN) ; Tafazzoli, M ; Sharif University of Technology
Abstract

Experimental and theoretical conformational study of repaglinide in chloroform and dimethyl sulfoxide was investigated. By applying potential energy scanning (PES) at B3LYP/6-311++g** and B3LYP-D3/6-311++g** level of theory on rotatable single bonds, four stable conformers (R1-R4) were identified. Spin-spin coupling constant values were obtained from a set of 2D NMR spectra (H[sbnd]H COSY, H[sbnd]C HMQC and H[sbnd]C HMBC) and compared to its calculated values. Interestingly, from 1HNMR and 2D-NOESY NMR, it has been found that repaglinide structure is folded in CDCl3 and cause all single bonds to rotate at an extremely slow rate. On the other hand, in DMSO-d6, with strong solvent-solute...

#### The Watershed Model and Schramm-loewner Evolution

, Ph.D. Dissertation Sharif University of Technology ; Rouhani, Shahin (Supervisor)
Abstract

Schramm Loewner evolution (SLE) is a one-parameter family of random simple curves in the complex plane introduced by Schramm in 1999 which is believed to describe the scaling limit of a variety of domain interfaces at criticality. This thesis is concerned with statistical properties of watersheds dividing drainage basins. The fractal dimension of this model is 1.22 which is consistent with the known fractal dimension for several important models such as Invasion percolation and minimum spanning trees (MST). We present numerical evidences that in the scaling limit this model are SLE curves with =1.73, being the only known physical example of an

SLE with <2. This lies outside the...

SLE with <2. This lies outside the...

#### Classification of Two-dimensional Surface Growth Models using Schramm -Loewner Evolution

, Ph.D. Dissertation Sharif University of Technology ; Rohani, Shahin (Supervisor) ; Saberi, Abbas Ali (Co-Advisor)
Abstract

Rough surfaces and growth process are the important and significant problems of theoretical and condensed matter physics to model phenomena ranging from the extremely small (biological phenomena) to largest one (Earth’s relief). Although the equations that describe these processes are well defined, but the question of how to characterize these surfaces which display large fluctuations, is open. The existence of (often) scale invariant clusters and very large fluctuations in surface growth process are reminiscent of critical fluctuations in equilibrium systems. Therefore, it is natural to try characterizing the surface by means of critical exponents, i.e., by the scaling dimensions of various...

#### Schrodinger-Virasoro Algebra

, M.Sc. Thesis Sharif University of Technology ; Rouhani, Shahin (Supervisor)
Abstract

This dissertation on the Schrodinger-Virasoro algebra will begin by a brief historical review on the development of the symmetry arguments and its final overwhelming success in the 20th century physics. Testifying many successes of symmetry arguments and group theoretic methods in physics such as the theory of relativity, many physicists began to ask whether covariance under a larger group of symmetry transformation would explain a broader era of physical phenomena? As will be reviewed in the beginning of the second chapter, invariance under conformal group - which includes Poincaré group as a subgroup and thus underlies Lorentzian geometry as its natural background geometry – has been...