20 research outputs found
Kerr-de Sitter Quasinormal Modes via Accessory Parameter Expansion
Quasinormal modes are characteristic oscillatory modes that control the
relaxation of a perturbed physical system back to its equilibrium state. In
this work, we calculate QNM frequencies and angular eigenvalues of Kerr--de
Sitter black holes using a novel method based on conformal field theory. The
spin-field perturbation equations of this background spacetime essentially
reduce to two Heun's equations, one for the radial part and one for the angular
part. We use the accessory parameter expansion of Heun's equation, obtained via
the isomonodromic -function, in order to find analytic expansions for the
QNM frequencies and angular eigenvalues. The expansion for the frequencies is
given as a double series in the rotation parameter and the extremality
parameter , where is the de Sitter radius and
and are the radii of, respectively, the cosmological and event
horizons. Specifically, we give the frequency expansion up to order
for general , and up to order with the
coefficients expanded up to . Similarly, the expansion for the
angular eigenvalues is given as a series up to with
coefficients expanded for small . We verify the new expansion for the
frequencies via a numerical analysis and that the expansion for the angular
eigenvalues agrees with results in the literature.Comment: 38+19 pages, 8 figures. v3: minor changes, matches published versio
Confinement in the q-state Potts model: an RG-TCSA study
In the ferromagnetic phase of the q-state Potts model, switching on an external magnetic field in- duces confinement of the domain wall excitations. For the Ising model (q = 2) the spectrum consists of kink-antikink states which are the analogues of mesonic states in QCD, while for q = 3, depending on the sign of the field, the spectrum may also contain three-kink bound states which are the analogues of the baryons. In recent years the resulting âhadronâ spectrum was described using several different approaches, such as quantum mechanics in the confining linear potential, WKB methods and also the Bethe-Salpeter equation. Here we compare the available predictions to numerical results from renor- malization group improved truncated conformal space approach (RG-TCSA). While mesonic states in the Ising model have already been considered in a different truncated Hamiltonian approach, this is the first time that a precision numerical study is performed for the 3-state Potts model. We find that the semiclassical approach provides a very accurate description for the mesonic spectrum in all the parameter regime for weak magnetic field, while the low-energy expansion from the Bethe-Salpeter equation is only valid for very weak fields where it gives a slight improvement over the semiclassical results. In addition, we confirm the validity of the recent predictions for the baryon spectrum obtained from solving the quantum mechanical three-body problem
PT breaking and RG flows between multicritical Yang-Lee fixed points
We study a novel class of Renormalization Group flows which connect
multicritical versions of the two-dimensional Yang-Lee edge singularity
described by the conformal minimal models M(2,2n+3). The absence in these
models of an order parameter implies that the flows towards and between
Lee-Yang edge singularities are all related to the spontaneous breaking of PT
symmetry and comprise a pattern of flows in the space of PT symmetric theories
consistent with the c-theorem and the counting of relevant directions.
Additionally, we find that while in a part of the phase diagram the domains of
unbroken and broken PT symmetry are separated by critical manifolds of class
M(2,2n+3), other parts of the boundary between the two domains are not
critical.Comment: 6 pages + supplemental materia
Multicriticality in Yang-Lee edge singularity
In this paper we study the non-unitary deformations of the two-dimensional
Tricritical Ising Model obtained by coupling its two spin \mathbb {Z}_2 odd
operators to imaginary magnetic fields. Varying the strengths of these
imaginary magnetic fields and adjusting correspondingly the coupling constants
of the two spin Z2 even fields, we establish the presence of two universality
classes of infrared fixed points on the critical surface. The first class
corresponds to the familiar Yang-Lee edge singularity, while the second class
to its tricritical version. We argue that these two universality classes are
controlled by the conformal non-unitary minimal models M(2,5) and M(2,7)
respectively, which is supported by considerations based on PT symmetry and the
corresponding extension of Zamolodchikov's c-theorem, and also verified
numerically using the truncated conformal space approach. Our results are in
agreement with a previous numerical study of the lattice version of the
Tricritical Ising Model [1]. We also conjecture the classes of universality
corresponding to higher non-unitary multicritical points obtained by perturbing
the conformal unitary models with imaginary coupling magnetic fields.Comment: 30 page
Variations on vacuum decay: The scaling Ising and tricritical Ising field theories
We study the decay of the false vacuum in the scaling Ising and tricritical Ising field theories using the truncated conformal space approach and compare the numerical results to theoretical predictions in the thin wall limit. In the Ising case, the results are consistent with previous studies on the quantum spin chain and the Ï4 quantum field theory; in particular, we confirm that while the theoretical predictions get the dependence of the bubble nucleation rate on the latent heat right, they are off by a model-dependent overall coefficient. The tricritical Ising model allows us on the other hand to examine more exotic vacuum degeneracy structures, such as three vacua or two asymmetric vacua, which leads us to study several novel scenarios of false vacuum decay by lifting the vacuum degeneracy using different perturbations
Confinement in the tricritical Ising model
We study the leading and sub-leading magnetic perturbations of the thermal E7 integrable deformation of the tricritical Ising model. In the low-temperature phase, these magnetic perturbations lead to the confinement of the kinks of the model. The resulting meson spectrum can be obtained using the semi-classical quantisation, here extended to include also mesonic excitations composed of two different kinks. An interesting feature of the integrable sub-leading magnetic perturbation of the thermal E7 deformation of the model is the possibility to swap the role of the two operators, i.e. the possibility to consider the model as a thermal perturbation of the integrable A3 model associated to the sub-leading magnetic deformation. Due to the occurrence of vacuum degeneracy unrelated to spontaneous symmetry breaking in A3, the confinement pattern shows novel features compared to previously studied models. Interestingly enough, the validity of the semi-classical description in terms of the A3 endpoint extends well beyond small fields, and therefore the full parameter space of the joint thermal and sub-leading magnetic deformation is well described by a combination of semi-classical approaches. All predictions are verified by comparison to finite volume spectrum resulting from truncated conformal space
Entanglement dynamics after a quench in Ising field theory: a branch point twist field approach
We extend the branch point twist field approach for the calculation of entanglement entropies to time-dependent problems in 1+1-dimensional massive quantum field theories. We focus on the simplest example: a mass quench in the Ising field theory from initial mass m0 to final mass m. The main analytical results are obtained from a perturbative expansion of the twist field one-point function in the post-quench quasi-particle basis. The expected linear growth of the RĂ©nyi entropies at large times mt â« 1 emerges from a perturbative calculation at second order. We also show that the RĂ©nyi and von Neumann entropies, in infinite volume, contain subleading oscillatory contributions of frequency 2m and amplitude proportional to (mt)â3/2. The oscillatory terms are correctly predicted by an alternative perturbation series, in the pre-quench quasi-particle basis, which we also discuss. A comparison to lattice numerical calculations carried out on an Ising chain in the scaling limit shows very good agreement with the quantum field theory predictions. We also find evidence of clustering of twist field correlators which implies that the entanglement entropies are proportional to the number of subsystem boundary points. © 2019, The Author(s)
On factorizable S-matrices, generalized TTbar, and the Hagedorn transition
We study solutions of the Thermodynamic Bethe Ansatz equations for relativistic theories defined by the factorizable S-matrix of an integrable QFT deformed by CDD factors. Such S-matrices appear under generalized TTbar deformations of integrable QFT by special irrelevant operators. The TBA equations, of course, determine the ground state energy E(R) of the finite-size system, with the spatial coordinate compactified on a circle of circumference R. We limit attention to theories involving just one kind of stable particles, and consider deformations of the trivial (free fermion or boson) S-matrix by CDD factors with two elementary poles and regular high energy asymptotics â the â2CDD modelâ. We find that for all values of the parameters (positions of the CDD poles) the TBA equations exhibit two real solutions at R greater than a certain parameter-dependent value R*, which we refer to as the primary and secondary branches. The primary branch is identified with the standard iterative solution, while the secondary one is unstable against iterations and needs to be accessed through an alternative numerical method known as pseudo-arc-length continuation. The two branches merge at the âturning pointâ R* (a square-root branching point). The singularity signals a Hagedorn behavior of the density of high energy states of the deformed theories, a feature incompatible with the Wilsonian notion of a local QFT originating from a UV fixed point, but typical for string theories. This behavior of E(R) is qualitatively the same as the one for standard TTbar deformations of local QFT
On factorizable S-matrices, generalized TTbar, and the Hagedorn transition
We study solutions of the Thermodynamic Bethe Ansatz equations for relativistic theories defined by the factorizable S-matrix of an integrable QFT deformed by CDD factors. Such S-matrices appear under generalized TTbar deformations of integrable QFT by special irrelevant operators. The TBA equations, of course, determine the ground state energy E(R) of the finite-size system, with the spatial coordinate compactified on a circle of circumference R. We limit attention to theories involving just one kind of stable particles, and consider deformations of the trivial (free fermion or boson) S-matrix by CDD factors with two elementary poles and regular high energy asymptotics â the â2CDD modelâ. We find that for all values of the parameters (positions of the CDD poles) the TBA equations exhibit two real solutions at R greater than a certain parameter-dependent value R*, which we refer to as the primary and secondary branches. The primary branch is identified with the standard iterative solution, while the secondary one is unstable against iterations and needs to be accessed through an alternative numerical method known as pseudo-arc-length continuation. The two branches merge at the âturning pointâ R* (a square-root branching point). The singularity signals a Hagedorn behavior of the density of high energy states of the deformed theories, a feature incompatible with the Wilsonian notion of a local QFT originating from a UV fixed point, but typical for string theories. This behavior of E(R) is qualitatively the same as the one for standard TTbar deformations of local QFT