The extremal metric method in the problem on the maximum of a conformal invariant

This chapter proves (1.17) when the worst terms in P(g) involve only factors of the differentiated Weyl tensor. This case is much harder than the previous one; in particular, in this case we need both a local conformal invariant W(g) and a divergence divᵢTⁱ(g) to prove (1.17). One obvious difficulty is how, upon inspection of P(g)subscript worst-piece, to separate the piece that must be cancelled out by a local conformal invariant from the piece that is cancelled out by a divergence. In a first step, we prove that we can first explicitly construct a local conformal invariant and a divergence and subtract them from P(g)subscript worst-piece, to be left with a new worst piece, which has some additional algebraic properties. In a second step, we show that this new worst piece can be cancelled out by subtracting a divergence.

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GRAVITY DUAL FOR REGGEON FIELD THEORY AND NONLINEAR QUANTUM FINANCE

International Journal of Modern Physics A ◽

10.1142/s0217751x09047594 ◽

2009 ◽

Vol 24 (32) ◽

pp. 6197-6222 ◽

Cited By ~ 12

Author(s):

YU NAKAYAMA

Keyword(s):

Field Theory ◽

Conformal Invariance ◽

Field Theories ◽

Conformal Field Theories ◽

Conformal Invariant ◽

Galilean Invariance ◽

Scale Invariant ◽

Conformal Field ◽

Nonlinear Quantum ◽

Reggeon Field Theory

We study scale invariant but not necessarily conformal invariant deformations of nonrelativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the nonrelativistic conformal invariance. We discuss applications to scaling regime of Reggeon field theory and nonlinear quantum finance. These theories possess scale invariance but may or may not break the conformal invariance, depending on the underlying symmetry assumptions.

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Unstable behaviors of classical solutions in spinor-type conformal invariant fermionic models

Journal of Experimental and Theoretical Physics ◽

10.1134/s1063776117100016 ◽

2017 ◽

Vol 125 (5) ◽

pp. 719-727 ◽

Cited By ~ 4

Author(s):

F. Aydogmus

Keyword(s):

Classical Solutions ◽

Conformal Invariant

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CORRELATION FUNCTIONS OF σ FIELDS WITH VALUES IN A HYPERBOLIC SPACE

International Journal of Modern Physics A ◽

10.1142/s0217751x8900011x ◽

1989 ◽

Vol 04 (01) ◽

pp. 267-286 ◽

Cited By ~ 9

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.

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