An exactly solvable two component classical Coulomb system

1984 ◽  
Vol 26 (2) ◽  
pp. 119-128 ◽  
Author(s):  
Peter J. Forrester
Keyword(s):  
Coulomb Potential ◽  
Correlation Functions ◽  
Asymptotic Form ◽  
Coulomb System ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Sum Rule ◽  
Exactly Solvable ◽  
Two Component ◽  
Special Value

AbstractA two component classical Coulomb system is considered, in which particles of charge +q and + 2q are constrained to lie on a circle and interact via the two-dimensional Coulomb potential. At a special value of the coupling constant the correlation functions are calculated exactly and the asymptotic form of the truncated charge-charge correlation is found to obey Jancovici's sum rule.

scholarly journals On 2d CFTs that interpolate between minimal models

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Structure Constants

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

scholarly journals UTILITY OF GALILEAN SYMMETRY IN LIGHT-FRONT PERTURBATION THEORY: A NONTRIVIAL EXAMPLE IN QCD

1998 ◽  
Vol 13 (26) ◽  
pp. 4591-4604 ◽  
Author(s):  
A. HARINDRANATH ◽  
RAJEN KUNDU
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Complex Structure ◽  
Light Front ◽  
Tree Level ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Two Component ◽  
Covariant Field ◽  
Galilean Symmetry

Investigations have revealed a very complex structure for the coefficient functions accompanying the divergences for individual time(x+)-ordered diagrams in light-front perturbation theory. No guidelines seem to be available to look for possible mistakes in the structure of these coefficient functions emerging at the end of a long and tedious calculation, in contrast to covariant field theory. Since, in light-front field theory, the transverse boost generator is a kinematical operator which acts just like the two-dimensional Galilean boost generator in nonrelativistic dynamics, it may provide some constraint on the resulting structures. In this work we investigate the utility of Galilean symmetry beyond tree level in the context of coupling constant renormalization in light-front QCD using the two-component formalism. We show that for each x+-ordered diagram separately, the underlying transverse boost symmetry fixes relative signs of terms in the coefficient functions accompanying the diverging logarithms. We also summarize the results leading to coupling constant renormalization for the most general kinematics.

scholarly journals POTENTIAL FLOW OF THE RENORMALIZATION GROUP IN A SIMPLE TWO-COMPONENT MODEL

1993 ◽  
Vol 08 (32) ◽  
pp. 3103-3110 ◽  
Author(s):  
BRIAN P. DOLAN
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Simple Model ◽  
Correlation Functions ◽  
Potential Flow ◽  
Dimensional Space ◽  
Component Model ◽  
Two Dimensional ◽  
Two Component ◽  
Point Correlation

The renormalization group (RG) flow on the space of couplings of a simple model with two couplings is examined. The model considered is that of a single component scalar field with φ4 self interaction coupled, via Yukawa coupling, to a fermion in flat four-dimensional space. The RG flow on the two-dimensional space of couplings, [Formula: see text], is shown to be derivable from a potential to sixth order in the couplings, which requires two-loop calculations of the β-functions. The identification of a potential requires the introduction of a metric on [Formula: see text] and it is shown that the metric defined by Zamolodchikov, in terms of two-point correlation functions of composite operators, gives potential flow to this order.

FREDHOLM DETERMINANT REPRESENTATION OF QUANTUM CORRELATION FUNCTION FOR SINE-GORDON AT SPECIAL VALUE OF COUPLING CONSTANT

1992 ◽  
Vol 06 (22) ◽  
pp. 1405-1411 ◽  
Author(s):  
H. ITOYAMA ◽  
V. E. KOREPIN ◽  
H. B. THACKER
Keyword(s):  
Correlation Functions ◽  
Fredholm Determinant ◽  
Free Fermion ◽  
Coupling Constant ◽  
Local Correlation ◽  
Determinant Representation ◽  
Special Value ◽  
Quantum Correlation Function ◽  
Sine Gordon Model ◽  
The One

Correlation functions of the Sine-Gordon model (which is equivalent to the Massive-Thirring model) are considered at the free fermion point. We derive a determinant formula for local correlation functions of the Sine-Gordon model, starting from Bethe ansatz wave function. Kernel of integral operator is trigonometric version of the one for Impenetrable Bosons.

SYMMETRY REORGANIZATION IN EXACTLY SOLVABLE TWO-DIMENSIONAL QUANTIZED SUPERGRAVITY

1989 ◽  
Vol 04 (09) ◽  
pp. 2245-2272 ◽  
Author(s):  
N.D. HARI DASS ◽  
R. SUMITRA
Keyword(s):  
Correlation Functions ◽  
Light Cone ◽  
Quantum Correlation ◽  
Two Dimensional ◽  
Supergravity Theory ◽  
Light Cone Gauge ◽  
Infinite Dimensional ◽  
Diffeomorphism Invariance ◽  
Supersymmetric Version ◽  
Exactly Solvable

A recent work of Polyakov solving exactly the two-dimensional induced quantum gravity is extended to the two-dimensional induced (1,0) quantum supergravity theory. This theory is found to be exactly integrable in a supersymmetric version of the light cone gauge. Solutions are found to display an infinite dimensional Z2 graded sl(2, R) invariance and a diffeomorphism invariance in one of the coordinates. The origin of these invariances is traced to motions along the gauge slice. A Sugawara construction based on the currents of the infinite dimensional transformations is shown to generate these diffeomorphisms. Explicit results are given for a number of quantum correlation functions.

scholarly journals Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yifei He ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Potts Model ◽  
Correlation Functions ◽  
Liouville Theory ◽  
Analytical Determination ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Conformal Blocks ◽  
Conformal Bootstrap ◽  
Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

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