scholarly journals DILATONIC GRAVITY NEAR TWO DIMENSIONS AS A STRING THEORY

1995 ◽  
Vol 10 (27) ◽  
pp. 2001-2008 ◽  
Author(s):  
E. ELIZALDE ◽  
S.D. ODINTSOV
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
String Theory ◽  
Sigma Model ◽  
Scalar Fields ◽  
Two Dimensions ◽  
Gravitational Coupling ◽  
Dilaton Coupling

Using the renormalization group formalism, a sigma model of a special type — in which the metric and the dilaton depend explicitly on one of the string coordinates only — is investigated near two dimensions. It is seen that dilatonic gravity coupled to N scalar fields can be expressed in this form, using a string parametrization, and that it possesses the usual uv fixed point. However, in this stringy parametrization of the theory the fixed point for the scalar-dilaton coupling turns out to be trivial, while that for the gravitational coupling remains the same as in previous studies being, in particular, nontrivial.

QUANTIZATION OF THE LIOUVILLE MODE AND STRING THEORY

1989 ◽  
Vol 04 (11) ◽  
pp. 1033-1041 ◽  
Author(s):  
SUMIT R. DAS ◽  
SATCHIDANANDA NAIK ◽  
SPENTA R. WADIA
Keyword(s):  
String Theory ◽  
Dimensional Space ◽  
Scalar Fields ◽  
Space Time ◽  
Two Dimensions ◽  
General Covariance ◽  
World Sheet ◽  
Lorentzian Signature ◽  
Dimensional Space Time ◽  
Background Fields

We discuss the space-time interpretation of bosonic string theories, which involve d scalar fields coupled to gravity in two dimensions, with a proper quantization of the world-sheet metric. We show that for d>25, the theory cannot describe string modes consistently coupled to each other. For d=25 this is possible; however, in this case the Liouville mode acts as an extra timelike variable and one really has a string moving in 26-dimensional space-time with a Lorentzian signature. By analyzing such a string theory in background fields, we show that the d=25 theory possesses the full 26-dimensional general covariance.

THE RENORMALIZATION OF THE NON-RENORMALIZABLE FOUR-DIMENSIONAL FOUR-FERMION INTERACTION

1993 ◽  
Vol 08 (09) ◽  
pp. 797-802 ◽  
Author(s):  
N.V. KRASNIKOV
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Scalar Fields ◽  
Renormalization Group Equations ◽  
Point Solution ◽  
Renormalizable Theory

We show that the non-renormalizable four-dimensional four-fermion Nambu interaction of color quarks can be renormalized. The non-renormalizable four-fermion interaction of color quarks is equivalent to the special (fixed-point) solution of the renormalization group equations for the renormalizable theory describing the interaction of the scalar fields with color quarks.

scholarly journals Statistical inference and string theory

2015 ◽  
Vol 30 (26) ◽  
pp. 1550160 ◽  
Author(s):  
Jonathan J. Heckman
Keyword(s):  
String Theory ◽  
Statistical Inference ◽  
Sigma Model ◽  
Two Dimensions ◽  
Nonlinear Sigma Model ◽  
Dimensional Manifold ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Lorentzian Signature ◽  
Stability Under Perturbations

In this paper, we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an [Formula: see text]-dimensional manifold of statistical fitting parameters. When the agents making nearby inferences align along a [Formula: see text]-dimensional grid, we find that the pooled probability that the collective reaches a correct inference is the partition function of a nonlinear sigma model in [Formula: see text] dimensions. Stability under perturbations to the original inference scheme requires the agents of the collective to distribute along two dimensions. Conformal invariance of the sigma model corresponds to the condition of a stable inference scheme, directly leading to the Einstein field equations for classical gravity. By summing over all possible arrangements of the agents in the collective, we reach a string theory. We also use this perspective to quantify how much an observer can hope to learn about the internal geometry of a superstring compactification. Finally, we present some brief speculative remarks on applications to the AdS/CFT correspondence and Lorentzian signature space–times.

scholarly journals GENERAL DILATONIC GRAVITY WITH AN ASYMPTOTICALLY FREE GRAVITATIONAL COUPLING CONSTANT NEAR TWO DIMENSIONS

1995 ◽  
Vol 10 (21) ◽  
pp. 1507-1519 ◽  
Author(s):  
E. ELIZALDE ◽  
S.D. ODINTSOV
Keyword(s):  
Fixed Point ◽  
General Theory ◽  
Two Dimensions ◽  
Gravitational Coupling ◽  
Quantum Level ◽  
Coupling Constant ◽  
Gravitational Coupling Constant ◽  
Scalar Matter ◽  
Free Scalar ◽  
The One

We study a renormalizable, general theory of dilatonic gravity (with a kinetic-like term for the dilaton) interacting with scalar matter near two dimensions. The one-loop effective action and the beta functions for this general theory are written down. It is proven that the theory possesses a nontrivial uv fixed point which yields an asymptotically free gravitational coupling constant (at ε→0) in this regime. Moreover, at the fixed point the theory can be cast under the form of a string-inspired model with free scalar matter. The renormalization of the Jackiw-Teitelboim model and of lineal gravity in 2+ε dimensions is also discussed. We show that these two theories are distinguished at the quantum level. Finally, fermion-dilatonic gravity near two dimensions is considered.

DILATON GRAVITY COUPLED TO A NONLINEAR SIGMA MODEL IN 2+ε DIMENSIONS

1995 ◽  
Vol 10 (32) ◽  
pp. 2391-2400
Author(s):  
SHIN-ICHI KOJIMA ◽  
NORISUKE SAKAI ◽  
YOSHIAKI TANII
Keyword(s):  
Fixed Point ◽  
Quantum Theory ◽  
Sigma Model ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Target Space ◽  
Nonlinear Sigma Model ◽  
Stable Fixed Point ◽  
Dilaton Gravity ◽  
Dilaton Coupling

Quantum theory of dilaton gravity coupled to a nonlinear sigma model with a maximally symmetric target space is studied in 2+ε dimensions. The uv stable fixed point for the curvature of the nonlinear sigma model demands a new fixed point theory for the dilaton coupling function. The fixed point of the dilaton coupling is a saddle point similarly to the previous case of the flat target space.

scholarly journals A proposal for studying off-shell stability of vacuum geometries in string theoryThis paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

2009 ◽  
Vol 87 (3) ◽  
pp. 213-217 ◽  
Author(s):  
V. Suneeta
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Sigma Model ◽  
Late Time ◽  
Time Behaviour ◽  
World Sheet ◽  
Shell Stability ◽  
Semiclassical Gravity ◽  
Related Approach ◽  
Well Posed

We briefly review studies of off-shell stability of vacuum geometries in semiclassical gravity. We propose a study of off-shell stability of vacua in string theory by a distinct, though somewhat related approach, by studying their stability under suitable world-sheet sigma model renormalization group (RG) flows. Stability under RG flow is a mathematically well-posed and tractable problem in many cases, as we illustrate through examples. The advantage is that we can make definite predictions about late time behaviour and endpoints of off-shell processes in string theory.

scholarly journals Some applications of Ricci flow in physics

2008 ◽  
Vol 86 (4) ◽  
pp. 645-651 ◽  
Author(s):  
E Woolgar
Keyword(s):  
General Relativity ◽  
Renormalization Group ◽  
Ricci Flow ◽  
Sigma Model ◽  
Final Section ◽  
Higher Dimensions ◽  
Ricci Soliton ◽  
Two Dimensions ◽  
Nonlinear Sigma Model

I discuss certain applications of the Ricci flow in physics. I first review how it arises in the renormalization group (RG) flow of a nonlinear sigma model. I then review the concept of a Ricci soliton and recall how a soliton was used to discuss the RG flow of mass in two dimensions. I then present recent results obtained with Oliynyk on the flow of mass in higher dimensions. The final section discusses how Ricci flow may arise in general relativity, particularly for static metrics.PACS Nos.: 02.40Ky, 02.30Ik, 04.20.–q

scholarly journals Symmetry breaking at high temperatures in large N gauge theories

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Soumyadeep Chaudhuri ◽  
Eliezer Rabinovici
Keyword(s):  
Fixed Point ◽  
Phase Transitions ◽  
Symmetry Breaking ◽  
High Temperatures ◽  
Gauge Theories ◽  
Scalar Fields ◽  
Temperature Limit ◽  
Spontaneous Breaking ◽  
Critical Temperatures ◽  
Weakly Coupled

Abstract Considering marginally relevant and relevant deformations of the weakly coupled (3 + 1)-dimensional large N conformal gauge theories introduced in [1], we study the patterns of phase transitions in these systems that lead to a symmetry-broken phase in the high temperature limit. These deformations involve only the scalar fields in the models. The marginally relevant deformations are obtained by varying certain double trace quartic couplings between the scalar fields. The relevant deformations, on the other hand, are obtained by adding masses to the scalar fields while keeping all the couplings frozen at their fixed point values. At the N → ∞ limit, the RG flows triggered by these deformations approach the aforementioned weakly coupled CFTs in the UV regime. These UV fixed points lie on a conformal manifold with the shape of a circle in the space of couplings. As shown in [1], in certain parameter regimes a subset of points on this manifold exhibits thermal order characterized by the spontaneous breaking of a global ℤ2 or U(1) symmetry and Higgsing of a subset of gauge bosons at all nonzero temperatures. We show that the RG flows triggered by the marginally relevant deformations lead to a weakly coupled IR fixed point which lacks the thermal order. Thus, the systems defined by these RG flows undergo a transition from a disordered phase at low temperatures to an ordered phase at high temperatures. This provides examples of both inverse symmetry breaking and symmetry nonrestoration. For the relevant deformations, we demonstrate that a variety of phase transitions are possible depending on the signs and magnitudes of the squares of the masses added to the scalar fields. Using thermal perturbation theory, we derive the approximate values of the critical temperatures for all these phase transitions. All the results are obtained at the N → ∞ limit. Most of them are found in a reliable weak coupling regime and for others we present qualitative arguments.

Sign in / Sign up

Export Citation Format

Share Document