Higher-derivative four-dimensional sine-Gordon model

Abstract

The phase structure of a higher derivative sine-Gordon model in four dimensions is analysed. It is shown that the inclusion of a relevant two-derivative term in the action significantly modifies some of the results obtained by neglecting this operator, and the final picture is substantially different from the one describing the phase diagram associated with the two-dimensional Berezinskii-Kosterlitz-Thouless (BKT) transition. The study is carried out with the help of the Renormalization Group (RG) flow equations, determined for a set of three parameters, and numerically solved both for a truncated series expansion approximation, and for the complete set of equations. In both cases, a continuous line of fixed points, terminating at a particular point presenting universal properties, is found, together with a manifold that separates two phases, roughly characterized by the sign of the coupling ${\tilde{z}}_k$ associated with this newly included operator. While the phase corresponding to ${\tilde{z}}_k>0$ shows some pathologies, the one with ${\tilde{z}}_k<0$ has a well-behaved infrared limit, where the system reduces to a Gaussian-like model. We also briefly comment about the possibility that our model could capture some of the qualitative features of the ultraviolet (UV) critical manifold of conformally reduced gravity.

24 pages, 7 figures. Published version

References in corpus (40)

• Quantum Gravity at a Lifshitz Point
• Exact evolution equation for the effective potential
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Living with Ghosts
• Inhomogeneous chiral condensates
• Quantum Criticality and Yang-Mills Gauge Theory
• Renormalization of Lorentz violating theories
• Field Theory at a Lifshitz Point
• Renormalization group in Lifshitz-type theories
• Background Independence and Asymptotic Safety in Conformally Reduced Gravity
• Fixed Points Structure & Effective Fractional Dimension for O(N) Models with Long-Range Interactions
• Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance
• Lifshitz-type Quantum Field Theories in Particle Physics
• Conformally reduced quantum gravity revisited
• Hořava gravity is asymptotically free (in 2+1 dimensions)
• Asymptotically free four-fermi theory in 4 dimensions at the z=3 Lifshitz-like fixed point
• Functional renormalization group approach to the sine-Gordon model
• Higher-derivative operators and effective field theory for general scalar-tensor theories
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
• How transverse thermal fluctuations disorder a condensate of chiral spirals into a quantum spin liquid
• Fixed point structure of the conformal factor field in quantum gravity
• Fluctuations in cool quark matter and the phase diagram of Quantum Chromodynamics
• Modulated Ground State of Gravity Theories with Stabilized Conformal Factor
• Nonperturbative functional renormalization-group approach to the sine-Gordon model and the Lukyanov-Zamolodchikov conjecture
• Comparison of renormalization group schemes for sine-Gordon type models
• Longitudinal fluctuations in the Berezinskii-Kosterlitz-Thouless phase
• Dual lattice functional renormalization group for the Berezinskii-Kosterlitz-Thouless transition: irrelevance of amplitude and out-of-plane fluctuations
• Critical, crossover, and correction-to-scaling exponents for isotropic Lifshitz points to order $(8-\mathbf{d}{)}^2$
• Effective potentials in the Lifshitz scalar field theory
• Scaling solutions in the derivative expansion
• Isotropic Lifshitz point in the O(N) Theory
• Isotropic Lifshitz critical behavior from the functional renormalization group
• Indications of isotropic Lifshitz points in four dimensions
• Topological phase transitions in four dimensions
• Restoration of Lorentz Symmetry for Lifshitz-Type Scalar Theory
• Physical properties of the massive Schwinger model from the nonperturbative functional renormalization group
• Isotropic Lifshitz Scaling in four dimensions
• Horava-Lifshitz Type Quantum Field Theory and Hierarchy Problem
• Lorentz symmetry violating Lifshitz-type field theories