An integrable Lorentz-breaking deformation of two-dimensional CFTs (1710.08415v3)

Abstract: It has been recently shown that the deformation of an arbitrary two-dimensional conformal field theory by the composite irrelevant operator $T \bar T$, built from the components of the stress tensor, is solvable; in particular, the finite-size spectrum of the deformed theory can be obtained from that of the original CFT through a universal formula. We study a similarly universal, Lorentz-breaking deformation of two-dimensional CFTs that posess a conserved $U(1)$ current, $J$. The deformation takes the schematic form $J \bar T$ and is interesting because it preserves an $SL(2,\mathbb{R}) \times U(1)$ subgroup of the original global conformal symmetries. For the case of a purely (anti)chiral current, we find the finite-size spectrum of the deformed theory and study its thermodynamic properties. We test our predictions in a simple example involving deformed free fermions.

An Integrable Lorentz-Breaking Deformation of Two-Dimensional CFTs

The paper investigates an integrable deformation of two-dimensional Conformal Field Theories (CFTs) that anomalously breaks Lorentz symmetry. This deformation leverages the presence of a conserved U(1) current and employs a deformation operator of the schematic form JT, where J represents the U(1) current, and T is related to the stress tensor of the original CFT.

Overview of the JT Deformation

The paper extends prior work on the TT deformation of two-dimensional CFTs, providing alternative paths to examine the richer algebraic structures in light of symmetry constraints. The JT deformation is postulated to preserve a subgroup of symmetries—namely, SL(2, R) × U(1), enhancing the theoretical framework set by typical CFT analyses. The authors utilize the deformation to derive the exact finite-size spectrum and thermodynamic properties of the deformed theory, delineating critical details of how JT modifies properties compared to established deformation paradigms.

Spectrum and Thermodynamics Analysis

By situating the theory on a cylinder, the paper navigates through the derivation of the finite-size spectrum and specific state energies. The reformulation entails eigenstate consideration of the Hamiltonian, momentum, and charge operators. Notably, the authors provide formulas for both left and right-moving energy contributions, thoroughly examining a specific class of examples involving free fermion systems.

In the chiral case, the deformation is found to induce a non-trivial shift in the spectrum by a field-dependent coordinate transformation on the base CFT, effectively marrying the left and right-moving aspects of the system. For the purely anti-chiral setting, the spectrum remains unaffected—an invariance attributed to the symmetry provided by pure antiholomorphic coordinate transformation. The resultant theory underscores significant thermodynamic consequences, including divergent behaviors in finite volume, stemming from the modified speed of excitations concurrent with the deformation.

Contrast with TT Deformation and Future Directions

From an integrability viewpoint, the JT deformation parallels the TT deformation but introduces distinct features due to its coupling with the U(1) current. Both deformations follow similar paths in renormalization group flow, although their implications on the UV completion and related scenarios diverge uniquely. The investigation suggests that JT may lead to fascinating modifications in asymptotic fragility, originally expounded within the TT framework in quantum gravity contexts.

Further exploration of the JT deformation aims to establish its role in theories of quantum gravity and its relevance in holography, particularly concerning the Kerr/CFT correspondence—a potential avenue for understanding transitions in 3D warped AdS holographies. The authors urge future studies to address symmetry enhancements, consider other U(1) current configurations, and explore broader implications in warped spacetime models.

Conclusion

The research identifies the JT deformation as a pivotal operator in two-dimensional quantum field theories, paving the way for novel interpretations of integrable deformations beyond conventional QFT landscapes. Subsequent investigations should strive to unravel the rich tapestry of correlational structures embedded within these deformations, emphasizing their potential impact on holographic dualities and advanced quantum theoretical models.