119126382
Twisting singular solutions of Betheʼs equations
The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.
119131032
Algebraic Bethe ansatz for singular solutions
The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N sites have solutions containing i/2, -i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions must be carefully regularized. We consider a regularization involving a parameter that can be determined using a generalization of the Bethe equations. These generalized Bethe equations provide a practical way of determining which singular solutions correspond to eigenvectors of the model.
119207341
Split flows in bubbled geometries
We propose a procedure to clarify part of the physical sector in the five dimensional bubble geometries based on ideas similar to the split attractor flow conjecture proposed by Denef. This procedure involves building some simple tree-like graphs that we call skeletons without referring to the moduli space. The skeleton (tree) exists if and only if it passes the existence conditions which are purely based on some local CTC’s (closed timelike curves) checking. Then, we propose the conjecture similar to Denef’s version which states that every existing skeleton (tree) should correspond to some solution in which the global absence of CTC’s is ensured. Furthermore, we propose two pictures to identify this correspondence explicitly and use some numerical examples to show how this procedure works. We also analyze the physical sector of the simplest bubbled supertube and see how the existence conditions constrain the charge parameter space.
118082738
Spinning Particles in Scalar-Tensor Gravity with Torsion
A new model of neutral spinning particles in scalar‐tensor gravity with torsion is developed by using a Fermi coordinates associated with orthonormal frames attached to a timelike curve and Noether identities. We further analyze its equations of motion both in background Brans‐Dicke torsion field and the constant pseudo‐Riemannian curvature with a constant scalar field. It turns that the particle’s spin vector is parallel transport along its wordline in the Brans‐Dicke torsion field and de Sitter spacetime. However, the dynamics of the spinning particle cannot completely determined in anti‐de Sitter spacetime and it requires a further investigation.
54005042
Modular properties of 3D higher spin theory
A bstractIn the three-dimensional $ \mathfrak{s}\mathfrak{l} $(N) Chern-Simons higher-spin theory, we prove that the conical surplus and the black hole solution are related by the S-transformation of the modulus of the boundary torus. Then applying the modular group on a given conical surplus solution, we generate a ‘SL(2, $ \mathbb{Z} $)’ family of smooth constant solutions. We then show how these solutions are mapped into one another by coordinate transformations that act non-trivially on the homology of the boundary torus.After deriving a thermodynamics that applies to all the solutions in the ‘SL(2, $ \mathbb{Z} $)’ family, we compute their entropies and free energies, and determine how the latter transform under the modular transformations. Summing over all the modular images of the conical surplus, we write down a (tree-level) modular invariant partition function.
119273603
Gravitational radiation and angular momentum flux from a spinning dynamical black hole
A four-dimensional asymptotic expansion scheme is used to s tudy the next order effects of the nonlinearity near a spinning dynamical black hole. The angu lar momentum flux and energy flux formula are then obtained by asymptotic expansion and th e compatibility of the coupling Newman-Penrose equations. After constructing the referen c frame in terms of the compatible constant spinors, the energy-momentum flux is derived and it is related to the black hole area growth. Directly from the flux formula of the spinning dynami cal horizon, we find that the physically reasonable condition on the positivity of the gr avitational energy flux yields that the shear will monotonically decrease with time.
17610587
Linearized Torsion Waves in a Tensor-Tensor Theory of Gravity
We investigate a linearized tensor-tensor theory of gravity with torsion and a perturbed torsion wave solution is discovered in background Minkowski spacetime with zero torsion. Furthermore, gauge transformations of any perturbed tensor field are derived in general background non-Riemannian geometries. By calculating autoparallel deviations, both longitudinal and transverse polarizations of the torsion wave are discovered.