We consider a truncation of the BMN matrix model to a configuration of two fuzzy spheres, described by two coupled non-linear oscillators dependent on the mass parameter $\textit{μ}$. The classical phase diagram of the system generically ($\textit{μ}$ ≠ 0) contains three equilibrium points: two centers and a center-saddle; as $\textit{μ}$ → 0 the system exhibits a pitchfork bifurcation. We demonstrate that the system is exactly integrable in quadratures for $\textit{μ}$ = 0, while for very large values of $\textit{μ}$, it approaches another integrable point characterized by two harmonic oscillators. The classical phase space is mixed, containing both integrable islands and chaotic regions, as evidenced by the classical Lyapunov spectrum. At the quantum level, we explore indicators of early and late time chaos. The eigenvalue spacing is best described by a Brody distribution, which interpolates between Poisson and Wigner distributions; it dovetails, at the quantum level, the classical results and reemphasizes the notion that the quantum system is mixed. We also study the spectral form factor and the quantum Lyapunov exponent, as defined by out-of-time-ordered correlators. These two indicators of quantum chaos exhibit weak correlations with the Brody distribution. We speculate that the behavior of the system as $\textit{μ}$ → 0 dominates the spectral form factor and the quantum Lyapunov exponent, making these indicators of quantum chaos less effective in the context of a mixed phase space.

Mexico

Paolo Amore

Italy

United States

Leopoldo Pando Zayas

Spain

Juan Pedraza

Norma Quiroz

César Terrero-Escalante

Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space

Anti-D3 branes and non-perturbative effects in flux compactifications spontaneously break supersymmetry and stabilise moduli in a metastable de Sitter vacua. The low energy 4D effective field theory description for such models would be a supergravity theory with non-linearly realised supersymmetry. Guided by string theory modular symmetry, we compute this non-linear supergravity theory, including dependence on all bulk moduli. Using either a constrained chiral superfield or a constrained vector field, the uplifting contribution to the scalar potential from the anti-D3 brane can be parameterised either as an F-term or Fayet-Iliopoulos D-term. Using again the modular symmetry, we show that 4D non-linear supergravities that descend from string theory have an enhanced protection from quantum corrections by non-renormalisation theorems. The superpotential giving rise to metastable de Sitter vacua is robust against perturbative string-loop and α ′ corrections.

Chile

Maria Garcia del Moral

United Kingdom

Susha Parameswaran

Ivonne Zavala

Anti-D3 branes and moduli in non-linear supergravity

We compute the left-right entanglement entropy for Dp-branes in string theory. We employ the CFT approach to string theory Dp-branes, in particular, its presentation as coherent states of the closed string sector. The entanglement entropy is computed as the von Neumann entropy for a density matrix resulting from integration over the left-moving degrees of freedom. We discuss various crucial ambiguities related to sums over spin structures and argue that different choices capture different physics; however, we advance a themodynamic argument that seems to favor a particular choice of replica. We also consider Dp branes on compact dimensions and verify that the effects of T-duality act covariantly on the Dp brane entanglement entropy. We find that generically the left-right entanglement entropy provides a suitable generalization of boundary entropy and of the D-brane tension.

Leopoldo Zayas

Left-right entanglement entropy of D p -branes

We study entanglement entropy of boundary states in a free bosonic conformal field theory. A boundary state can be thought of as composed of a particular combination of left and right-moving modes of the two-dimensional conformal field theory. We investigate the reduced density matrix obtained by tracing over the right-moving modes in various boundary states. We consider Dirichlet and Neumann boundary states of a free noncompact as well as a compact boson. The results for the entanglement entropy indicate that the reduced system can be viewed as a thermal CFT gas. Our findings are in agreement and generalize results in quantum mechanics and quantum field theory where coherent states can also be considered. In the compact case we verify that the entanglement entropy expressions are consistent with T-duality.

Left-right entanglement entropy of boundary states