Stiffness dependence of deconfinement transition for strings with extrinsic curvature term

1989 ◽  
Vol 225 (1-2) ◽  
pp. 107-111 ◽  
Author(s):  
G. Germán ◽  
H. Kleinert
Keyword(s):  
Extrinsic Curvature ◽  
Curvature Term

scholarly journals SPECTRUM OF THE LOOP TRANSFER MATRIX ON FINITE LATTICES

2001 ◽  
Vol 16 (16) ◽  
pp. 1069-1077 ◽  
Author(s):  
GEORGIOS DASKALAKIS ◽  
GEORGE K. SAVVIDY
Keyword(s):  
Transfer Matrix ◽  
Phase Structure ◽  
Extrinsic Curvature ◽  
Critical Behaviour ◽  
Equivalent Representation ◽  
Random Surfaces ◽  
Finite Dimensional ◽  
Curvature Term ◽  
Finite Lattices ◽  
Euclidean Lattice

We consider a model of random surfaces with extrinsic curvature term embedded into 3-D Euclidean lattice Z3. On a 3-D Euclidean lattice it has an equivalent representation in terms of the transfer matrix K(Qi, Qf), which describes the propagation of the loops Q. We study the spectrum of the transfer matrix K(Qi, Qf) on finite-dimensional lattices. The renormalisation group technique is used to investigate the phase structure of the model and its critical behaviour.

scholarly journals Stiff self-interacting strings at high temperature QCD

2018 ◽  
Vol 175 ◽  
pp. 12004
Author(s):  
A. S Bakry ◽  
X. Chen ◽  
M. Deliyergiyev ◽  
A. Galal ◽  
A. Khalaf ◽  
...  
Keyword(s):  
Lattice Gauge Theory ◽  
Extrinsic Curvature ◽  
Casimir Energy ◽  
Monte Carlo Data ◽  
Yang Mills ◽  
Lattice Monte Carlo ◽  
Lattice Gauge ◽  
Curvature Term ◽  
Intermediate Distance ◽  
Qcd String

We investigate the implications of Nambu-Goto (NG), Lüscher Weisz (LW) and Polyakov-Kleinert (PK) effective string actions for the Casimir energy and the width of the quantum delocalization of the string in 4-dim pure SU(3) Yang-Mills lattice gauge theory. At a temperature closer to the critical point T/Tc=0.9, we found that the next to leading-order (NLO) contributions from the expansion of the NG string in addition to the boundary terms in LW action to decrease the deviations from the lattice data in the intermediate distance scales for both the quark-antiquark QQ̅ potential and broadening of the color tube compared to the free string approximation. We conjecture possible stiffness of the QCD string through studying the effects of extrinsic curvature term in PK action and find a good fitting behavior for the lattice Monte-Carlo data at both long and intermediate quark separations regions.

scholarly journals RENORMALIZATION OF COUPLINGS IN EMBEDDED RANDOM SURFACES

1992 ◽  
Vol 07 (40) ◽  
pp. 3747-3757
Author(s):  
SUMIT R. DAS ◽  
S. KALYANA RAMA
Keyword(s):  
Phase Space ◽  
Extra Dimension ◽  
Extrinsic Curvature ◽  
String Tension ◽  
Length Scale ◽  
Random Surfaces ◽  
Curvature Term ◽  
Composite Field ◽  
Physical Scale ◽  
The Relationship

We study the dressing of operators and flows of corresponding couplings in models of embedded random surfaces. We show that these dressings can be obtained by applying the methods of David and Distler and Kawai. We consider two extreme limits. In the first limit the string tension is large and the dynamics is dominated by the Nambu-Goto term. We analyze this theory around a classical solution in the situation where the length scale of the solution is large compared to the length scale set by the string tension. Couplings get dressed by the Liouville mode (which is now a composite field) in a non-trivial fashion. However this does not imply that the excitations around a physical “long string” have a phase space corresponding to an extra dimension. In the second limit the string tension is small and the dynamics is governed by the extrinsic curvature term. We show, perturbatively, that in this theory the relationship between the induced metric and the worldsheet metric is “renormalized,” while the extrinsic curvature term receives a non-trivial dressing as well. This has the consequence that in a generic situation the dependence of couplings on the physical scale is different from that predicted by their beta functions.

STATISTICAL MECHANICS OF A RIGID BUBBLE: HIGHER DERIVATIVE QUANTUM GRAVITY ON A SPHERICAL RANDOM SURFACE EMBEDDED IN E3

1989 ◽  
Vol 04 (25) ◽  
pp. 2417-2428 ◽  
Author(s):  
HIROSHI KOIBUCHI ◽  
MITSURU YAMADA
Keyword(s):  
Correlation Energy ◽  
Three Dimensional ◽  
Extrinsic Curvature ◽  
Ideal Gas ◽  
Dimensional Euclidean Space ◽  
Rigid Surface ◽  
Random Surface ◽  
Higher Derivative ◽  
Curvature Term ◽  
Normal Vectors

A model of rigid surface of S2 topology embedded in a three-dimensional Euclidean space E3 is numerically studied. The action of the model has an extrinsic curvature term SEC in addition to the two-dimensional higher derivative gravity action. Since the SEC is thought of as the correlation energy of the normal vectors of the surface, it is discretized by an analogy to the σ model. The expected ideal gas behavior of the model can be seen from the Monte Carlo results at sufficiently low temperatures. The phase structure of the model is investigated and it is found that the SEC in the action causes some phase transition at an intermediate temperature.

scholarly journals The Kerr-Schild double copy in Lifshitz spacetime

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Gökhan Alkaç ◽  
Mehmet Kemal Gümüş ◽  
Mustafa Tek
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Charge Density ◽  
Localized Source ◽  
Curvature Term ◽  
Constant Charge Density ◽  
Arbitrary Dimensions ◽  
Double Copy ◽  
Theory Solution ◽  
Constant Charge

Abstract The Kerr-Schild double copy is a map between exact solutions of general relativity and Maxwell’s theory, where the nonlinear nature of general relativity is circumvented by considering solutions in the Kerr-Schild form. In this paper, we give a general formulation, where no simplifying assumption about the background metric is made, and show that the gauge theory source is affected by a curvature term that characterizes the deviation of the background spacetime from a constant curvature spacetime. We demonstrate this effect explicitly by studying gravitational solutions with non-zero cosmological constant. We show that, when the background is flat, the constant charge density filling all space in the gauge theory that has been observed in previous works is a consequence of this curvature term. As an example of a solution with a curved background, we study the Lifshitz black hole with two different matter couplings. The curvature of the background, i.e., the Lifshitz spacetime, again yields a constant charge density; however, unlike the previous examples, it is canceled by the contribution from the matter fields. For one of the matter couplings, there remains no additional non-localized source term, providing an example for a non-vacuum gravity solution corresponding to a vacuum gauge theory solution in arbitrary dimensions.

scholarly journals HIGHER-ORDER CURVATURE TERMS IN BORN–INFELD TYPE BRANE THEORIES

2011 ◽  
Vol 20 (01) ◽  
pp. 59-75 ◽  
Author(s):  
EFRAIN ROJAS
Keyword(s):  
Ricci Tensor ◽  
General Structure ◽  
Extrinsic Curvature ◽  
Higher Order ◽  
Square Root ◽  
Auxiliary Variables ◽  
Field Equations ◽  
Alternative Description ◽  
Brane Models ◽  
Combined Matrix

The field equations associated to Born–Infeld type brane theories are studied by using auxiliary variables. This approach hinges on the fact, that the expressions defining the physical and geometrical quantities describing the worldvolume are varied independently. The general structure of the Born–Infeld type theories for branes contains the square root of a determinant of a combined matrix between the induced metric on the worldvolume swept out by the brane and a symmetric/antisymmetric tensor depending on gauge, matter or extrinsic curvature terms taking place on the worldvolume. The higher-order curvature terms appearing in the determinant form come to play in competition with other effective brane models. Additionally, we suggest a Born–Infeld–Einstein type action for branes where the higher-order curvature content is provided by the worldvolume Ricci tensor. This action provides an alternative description of the dynamics of braneworld scenarios.

COVARIANT CONFORMAL DECOMPOSITION OF EINSTEIN EQUATIONS

2002 ◽  
Vol 17 (20) ◽  
pp. 2762-2762
Author(s):  
E. GOURGOULHON ◽  
J. NOVAK
Keyword(s):  
Numerical Simulations ◽  
Extrinsic Curvature ◽  
Einstein Equations ◽  
Numerical Implementation ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Tensor Density ◽  
Dirac Gauge ◽  
Ill Posed ◽  
Isolated Systems

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-"metric" (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this "metric", of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

scholarly journals ON EIGENVALUE ESTIMATES FOR THE SUBMANIFOLD DIRAC OPERATOR

2002 ◽  
Vol 13 (05) ◽  
pp. 533-548 ◽  
Author(s):  
NICOLAS GINOUX ◽  
BERTRAND MOREL
Keyword(s):  
Dirac Operator ◽  
Lower Bounds ◽  
Dirac Operators ◽  
Extrinsic Curvature ◽  
Eigenvalue Estimates ◽  
Killing Spinors ◽  
Spinor Fields ◽  
Twisted Dirac Operators

We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class of spinor fields generalizing that of Killing spinors. We conclude by translating these results in terms of intrinsic twisted Dirac operators.

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