Higher Spin Modes Research Articles

Spherically symmetric solutions of higher-spin gravity in the IKKT matrix model

We present a systematic study of spherically symmetric vacuum solutions of the IKKT matrix model, within the framework of semi-classical covariant quantum geometries. All asymptotically flat solutions of the equations of motion of the frame are found explicitly. They reproduce the linearized Schwarzschild geometry for large r but deviate from it at the non-linear level, and include contributions from dilaton and axion. They are pertinent to the pre-gravity theory arising on classical brane solutions within the classical matrix model, before taking into account the Einstein-Hilbert term induced by quantum effects. We also address the problem of reconstructing matrix configurations corresponding to some given frame, and show that this problem can always be solved at the geometrical level of the underlying higher spin theory, ignoring possible higher spin modes.

Gravity as a quantum effect on quantum space-time

The 3+1-dimensional Einstein-Hilbert action is obtained from the 1-loop effective action on noncommutative branes in the IIB or IKKT matrix model. The presence of compact fuzzy extra dimensions K as well as maximal supersymmetry of the model is essential. The E-H action can be interpreted as interaction of K with the space-time brane via IIB supergravity, and the effective Newton constant is determined by the Kaluza-Klein scale of K. The classical matrix model defines a pre-gravity action with 2 derivatives less than the induced E-H action, governing the cosmological regime. The perturbative physics is confined to the space-time brane, which for covariant quantum space-times includes all dof of gravity, as well as a tower of higher-spin modes. The vacuum energy of the background is given in terms of the symplectic volume form, and hence does not act as cosmological constant.

Chaos in three-dimensional higher spin gravity

We discuss SL(N, ℂ) Chern-Simons higher spin gauge theories in Euclidean AdS3. With appropriate boundary term, we derive the higher spin generalization of Schwarzian on-shell action. We investigate gravitationally dressed bi-locals, and we study the soft higher spin mode expansion to obtain soft mode eigenfunctions. We also derive the spin-s eigenfunction from Ward identity of mathcal{W} -algebra and a recursion relation. Using the on-shell action, we evaluate the contributions of the soft higher spin modes to the out-of-time-order correlators, and the corresponding Lyapunov exponent of SL(N) higher spin gravity is found to be frac{2pi }{beta}left(N - 1right) .

Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model

We discuss a (3+1)-dimensional covariant quantum space-time describing a FLRW cosmology with Big Bounce, obtained by a projection of the fuzzy hyperboloid Hn4. This provides a background solution of the IKKT matrix model with mass term. We characterize the bosonic fluctuation spectrum, which consists of a tower of higher-spin modes, truncated at n. The modes are organized in terms of an underlying SO(4, 2) structure group, which is broken to the SO(3, 1) isometry of the background. The resulting higher-spin gauge theory includes all degrees of freedom required for gravity, and should be well suited for quantization. All modes propagate with the same speed of light, even though local boost invariance is not manifest. The propagating metric perturbation modes comprise those of a massless graviton, as well as a scalar mode. Gauge invariance allows to obtain the analog of the linearized Einstein-Hilbert action, which is expected to be induced upon quantization.

The fuzzy 4-hyperboloid [formula omitted] and higher-spin in Yang–Mills matrix models

We consider the SO(4,1)-covariant fuzzy hyperboloid Hn4 as a solution of Yang–Mills matrix models, and study the resulting higher-spin gauge theory. The degrees of freedom can be identified with functions on classical H4 taking values in a higher-spin algebra associated to so(4,1), truncated at spin n. We develop a suitable calculus to classify the higher-spin modes, and show that the tangential modes are stable. The metric fluctuations encode one of the spin 2 modes, however they do not propagate in the classical matrix model. Gravity is argued to arise upon taking into account induced gravity terms. This formalism can be applied to the cosmological FLRW space-time solutions of [1], which arise as projections of Hn4. We establish a one-to-one correspondence between the tangential fluctuations of these spaces.

Higher spin modes as rolling tachyons in open string field theory

We find a simple analytic solution in open string field theory which, in the on-shell limit, generates a tower of higher spin vertex operators in bosonic string theory. The solution is related to irregular off-shell vertex operators for Gaiotto states. The wavefunctions for the irregular vertex operators are described by equations following from the cubic effective action for generalized rolling tachyons, indicating that the evolution from flat to collective higher-spin background in string field theory occurs according to cosmological pattern. We discuss the relation between nonlocalities of the rolling tachyon action and those of higher spin interactions.

New analytic solutions in string field theory: Towards a collective higher spin vacuum

We construct analytic solutions in cubic open superstring field theory at higher superconformal ghost numbers.The solutions are the pure ghost ones and are given by combinations of Bell polynomials of bosonized superconformal ghost fields multiplied by exponents of the bosonized ghosts. Based on the structure of the solutions, we conjecture them to describe the ghost part of collective vacuum for higher spin modes in open string theory.

Temperature-induced emergence of Wigner correlations in a STM-probed one-dimensional quantum dot

The temperature-induced emergence of Wigner correlations over finite-size effects in a strongly interacting one-dimensional quantum dot is studied in the framework of the spin coherent Luttinger liquid. We demonstrate that, for temperatures comparable with the zero mode spin excitations, Friedel oscillations are suppressed by the thermal fluctuations of higher spin modes. On the other hand, the Wigner oscillations, sensitive to the charge mode only, are stable and become more visible. This behavior has been proved to be robust both in the thermal electron density and in the linear conductance in the presence of a scanning tunnel microscope tip. The latter probe is not directly proportional to the electron density and may confirm the above phenomena with complementary and additional information.

Current Exchanges for Reducible Higher Spin Modes on AdS

We show how to decompose a Lagrangian for reducible massless bosonic Higher Spin modes into the ones describing irreducible (Fronsdal) Higher Spin modes on a D dimensional AdS space. Using this decomposition we construct a new nonabelian cubic interaction vertex for reducible higher spin modes and two scalars on AdS from the already known vertex which involves irreducible (Fronsdal) modes

HAMILTONIAN ANALYSIS OF POINCARÉ GAUGE THEORY: HIGHER SPIN MODES

We examine several higher spin modes of the Poincaré gauge theory (PGT) of gravity using the Hamiltonian analysis. The appearance of certain undesirable effects due to nonlinear constraints in the Hamiltonian analysis are used as a test. We find that the phenomena of field activation and constraint bifurcation both exist in the pure spin 1 and the pure spin 2 modes. The coupled spin-0- and spin-2- modes also fail our test due to the appearance of constraint bifurcation. The "promising" case in the linearized theory of the PGT given by Kuhfuss and Nitsch1 likewise does not pass. From this analysis of these specific PGT modes we conclude that an examination of such nonlinear constraint effects shows great promise as a strong test for this and other alternate theories of gravity.

One-loop renormalization of higher-derivative 2D dilaton gravity

A theory of higher-derivative 2D dilaton gravity which has its roots in the massive higher-spin mode dynamics of string theory is suggested. The divergences of the effective action to one-loop are calculated, both in the covariant and in the conformal gauge. Some technical problems which appear in the calculations are discussed. An interpretation of the theory as a particular D = 2 higher-derivative σ-model is given. for a specific case of higher-derivative 2D dilaton gravity, which is one loop multiplicatively renormalizable, static configurations corresponding to black holes are shown to exist.