CORRELATION FUNCTIONS OF σ FIELDS WITH VALUES IN A HYPERBOLIC SPACE

1989 ◽  
Vol 04 (01) ◽  
pp. 267-286 ◽  
Author(s):  
Z. HABA
Keyword(s):  
Field Theory ◽  
Hyperbolic Space ◽  
Half Plane ◽  
Correlation Functions ◽  
Functional Integral ◽  
Two Dimensions ◽  
Hyperbolic Spaces ◽  
Conformal Invariant ◽  
Upper Half Plane

It is shown that the functional integral for a σ field with values in the Poincare upper half-plane (and some other hyperbolic spaces) can be performed explicitly resulting in a conformal invariant noncanonical field theory in two dimensions.

CONFORMALLY INVARIANT FIELD THEORY IN TWO DIMENSIONS AND STRINGS IN CURVED SPACETIME

1988 ◽  
Vol 03 (08) ◽  
pp. 1759-1846 ◽  
Author(s):  
SANJAY JAIN
Keyword(s):  
Field Theory ◽  
Equations Of Motion ◽  
Virasoro Algebra ◽  
Functional Integral ◽  
Two Dimensions ◽  
Intrinsic Metric ◽  
Existence Of A Solution ◽  
Conformally Invariant ◽  
Brst Charge ◽  
Spacetime Metric

The formalism of conformally invariant field theory on a 2-dimensional real manifold with an intrinsic metric is developed in the functional integral framework. This formalism is used to study the relationships between reparametrization, Weyl, conformal and BRST invariances for strings in generic backgrounds. Conformal invariance of string amplitudes in the presence of backgrounds is formulated in terms of the Virasoro conditions, i.e., that physical vertex operators generate (1,1) representations of the Virasoro algebra, or, equivalently, the condition Q|Ψ〉=0 on physical states |Ψ〉, where Q is the BRST charge. The consequences of these conditions are investigated in the case of specific backgrounds. Strings in group manifolds are discussed exactly. For a generic slowly varying spacetime metric and dilaton field, a perturbatively renormalized vertex operator solution to the Virasoro conditions is constructed. It is shown that the existence of a solution to the Virasoro conditions or the equation Q|Ψ〉=0 requires the spacetime metric to satisfy Einstein’s equations. These conditions therefore constitute equations of motion for both the spectrum and backgrounds of string theory.

scholarly journals ON THE LIOUVILLE APPROACH TO CORRELATION FUNCTIONS FOR 2D QUANTUM GRAVITY

1992 ◽  
Vol 07 (03) ◽  
pp. 235-249 ◽  
Author(s):  
KENICHIRO AOKI ◽  
ERIC D’HOKER
Keyword(s):  
Quantum Gravity ◽  
Correlation Functions ◽  
Functional Integral ◽  
Two Dimensions ◽  
Minimal Models ◽  
Point Function

We evaluate the three-point function for arbitrary states in bosonic minimal models on the sphere coupled to quantum gravity in two dimensions. The validity of the formal continuation in the number of Liouville screening charge insertions is shown directly from the Liouville functional integral using semi-classical methods.

scholarly journals RECENT DEVELOPMENTS IN D=2 STRING FIELD THEORY

1994 ◽  
Vol 09 (18) ◽  
pp. 3103-3141 ◽  
Author(s):  
MICHIO KAKU
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Correlation Functions ◽  
Two Dimensions ◽  
Field Theories ◽  
Fermion Field ◽  
Free Fermion ◽  
Temporal Gauge ◽  
Recent Developments ◽  
The Relationship

We review the recent developments in the construction of string field theory in two dimensions. We analyze the bewildering number of string field theories that have been proposed, all of which correctly reproduce the correlation functions of two-dimensional string theory. These include (1) free fermion field theory, (2) collective string field theory, (3) temporal gauge string field theory and (4) nonpolynomial string field theory. We will analyze discrete states, the ω(∞) symmetry, and correlation functions in terms of these different string field theories. We will also comment on the relationship between these field theories, which is still not well understood.

GLUING THEOREM, STAR PRODUCT AND INTEGRATION IN OPEN STRING FIELD THEORY IN ARBITRARY BACKGROUND FIELDS

1991 ◽  
Vol 06 (30) ◽  
pp. 5387-5407 ◽  
Author(s):  
A.S. SCHWARZ ◽  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Half Plane ◽  
String Field Theory ◽  
Central Charge ◽  
Star Product ◽  
Open String ◽  
Conformal Field ◽  
Upper Half Plane ◽  
Background Fields

We discuss how to define star product and integration in a string field theory formulated in a background provided by an arbitrary conformal field theory on the upper half-plane with central charge 26.

scholarly journals THE FREE FIELD REPRESENTATION OF SU(3) CONFORMAL FIELD THEORY

1993 ◽  
Vol 08 (23) ◽  
pp. 4031-4053
Author(s):  
HOVIK D. TOOMASSIAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Free Field ◽  
Field Representation ◽  
Conformal Field ◽  
Point Correlation

The structure of the free field representation and some four-point correlation functions of the SU(3) conformal field theory are considered.

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

scholarly journals Extremal correlators and random matrix theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Alba Grassi ◽  
Zohar Komargodski ◽  
Luigi Tizzano
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Matrix Model ◽  
Effective Field Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Matrix Theory ◽  
Effective Field ◽  
Random Matrix Model ◽  
Large Charge

Abstract We study the correlation functions of Coulomb branch operators of four-dimensional $$ \mathcal{N} $$ N = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.

scholarly journals Interface Roughening in Two Dimensions

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Gernot Münster ◽  
Manuel Cañizares Guerrero
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Capillary Wave ◽  
System Size ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Wave Approximation ◽  
Statistical Field ◽  
Statistical Field Theory ◽  
Interface Roughening

AbstractRoughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of $$w^2$$ w 2 is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of $$w^2$$ w 2 , which differs from results in the literature. It is confirmed by Monte Carlo simulations.

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