Deformed integrable models from holomorphic Chern-Simons theory

We study the approaches to two-dimensional integrable field theories via a six-dimensional(6 D) holomorphic Chern-Simons theory defined on twistor space. Under symmetry reduction, it reduces to a 4 D Chern-Simons theory, while under solving along fibres it leads to a four-dimensional(4 D) integrable theory, the anti-self-dual Yang-Mills or its generalizations. From both 4 D theories, various two-dimensional integrable field theories can be obtained. In this work, we try to investigate several twodimensional integrable deformations in this framework. We find that the λ-deformation, the rational η-deformation, and the generalized λ-deformation can not be realized from the 4 D integrable model approach, even though they could be obtained from the 4 D Chern-Simons theory. The obstacle stems from the incompatibility between the symmetry reduction and the boundary conditions. Nevertheless, we show that a coupled theory of the λ-deformation and the η-deformation in the trigonometric description could be obtained from the 6 D theory in both ways, by considering the case that(3, 0)-form in the 6 D theory is allowed to have zeros.

Lax connections in TT-deformed integrable field theories

In this work,we attempt to construct the Lax connections of TT-deformed integrable field theories in two different ways.With reasonable assumptions,we make an ansatz and find the Lax pairs in the TT-deformed affine Toda theories and the principal chiral model by solving the Lax equations directly.This method is straightforward,but it may be difficult to apply for general models.We then make use of a dynamic coordinate transformation to read the Lax connection in the deformed theory from the undeformed one.We find that once the inverse of the transformation is available,the Lax connection can be read easily.We show the construction explicitly for a few classes of scalar models and find consistency with those determined using the first method.

More on half-wormholes and ensemble averages

We continue our study Half-Wormholes and Ensemble Averages about the half-wormhole proposal.By generalizing the original proposal of the half-wormhole,we propose a new way to detect half-wormholes.The crucial idea is to decompose the observables into self-averaged sectors and non-self-averaged sectors.We find the contributions from different sectors have interesting statistics in the semi-classical limit.In particular,dominant sectors tend to condense and the condensation explains the emergence of half-wormholes and we expect that the appearance of condensation is a signal of possible bulk description.We also initiate the study of multi-linked half-wormholes using our approach.

Implications of gamma-ray photon measurements at the LHAASO on Lorentz symmetry

The Large High Altitude Air Shower Observatory(LHAASO)has reported the measurement of photons with high energies of up to 1.42 PeV from twelve gamma-ray sources.We are concerned with the implications of the LHAASO data on the fate of Lorenz symmetry at such high energy levels;thus,we consider the interaction between gamma rays and photons in the cosmic microwave background(CMB)and compute the optical depth,mean free path,and survival probability of photons from these gamma-ray sources.Employing the threshold value predicted by standard special relativity,the lowest survival probability for observed gamma ray photons is found to be approximately 0.60,which is fairly high and implies that abundant photons with energies above the threshold may reach the Earth without Lorentz symmetry violation.We conclude that it is unreasonable to argue that Lorentz symmetry would be violated using current observations at the LHAASO.