Boundary-value problems in RG flows are not always unique when the beta-function Jacobian has complex eigenvalues, unlike initial-value problems, with a diagnostic tool and examples in the SM and ASQG.
Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
4 Pith papers cite this work, alongside 481 external citations. Polarity classification is still indexing.
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abstract
For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N=1 supersymmetric gauge theory. Exact, explicit formulas for $SU(N_c)$ gauge theories in the conformal window are given and analysed. The Euler anomaly coefficient always satisfies the inequality $% a_{UV}-a_{IR}>0$. This is new evidence in strongly coupled theories that this quantity satisfies a four-dimensional analogue of the $c$-theorem, supporting the idea of irreversibility of the RG flow. Various other implications are discussed.
fields
hep-th 4representative citing papers
The paper proposes that condensate competition in the 2d Gross-Neveu model generates an emergent AdS₃ bulk, a higher-spin tower, D1-branes, and linearized Einstein gravity with G₃ = ℓ_AdS/4πN².
Explicit closed-form evaluation of A(n) and B(m) for exponential regulators R(x)=e^{x^n} and F(x)=e^{x^m} yields fully parameterized three-loop beta functions in general N=1 SUSY gauge theories and demonstrates finite redefinitions mapping to an NSVZ-compatible scheme.
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Non-uniqueness of boundary-value problems in Renormalization Group flows
Boundary-value problems in RG flows are not always unique when the beta-function Jacobian has complex eigenvalues, unlike initial-value problems, with a diagnostic tool and examples in the SM and ASQG.
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Higher-spin composites and emergent AdS$_3$ geometry in the $(1+1)$-dimensional Gross-Neveu model
The paper proposes that condensate competition in the 2d Gross-Neveu model generates an emergent AdS₃ bulk, a higher-spin tower, D1-branes, and linearized Einstein gravity with G₃ = ℓ_AdS/4πN².
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Three-Loop Gauge Beta Functions in Supersymmetric Theories with Exponential Higher Covariant Derivative Regularization
Explicit closed-form evaluation of A(n) and B(m) for exponential regulators R(x)=e^{x^n} and F(x)=e^{x^m} yields fully parameterized three-loop beta functions in general N=1 SUSY gauge theories and demonstrates finite redefinitions mapping to an NSVZ-compatible scheme.
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