In this article, we present explicit evidence that maximal chaos occurs for a generic, probe quark-like defect degrees of freedom, in a strongly coupled large $N_c$ gauge theory. In holography, this corresponds to the dynamics of open string degrees of freedom, in the background of a closed string geometry. In this context, we explicitly show that a Schwarzian effective action for the soft sector emerges and couples with other modes, in the infra-red. This is manifest on an open string worldsheet, as well as a D$1$-brane world-volume, embedded in AdS$_3$. The corresponding maximal chaos is governed by an intrinsic defect D-brane horizon, and an intrinsic non-linear description of the brane or the string. We also present explicit evidence of maximal chaos away from extremality on a D-brane horizon, by computing a four-point out-of-time order correlator of spin-one operators. This further suggests that a similar description of the soft sector physics of open string degrees of freedom may exist in general.
We discuss the quantum correction to chaos in the Schwarzian theory. We carry out the semi-classical analysis of the Schwarzian theory to study Feynman diagrams of the Schwarzian soft mode. We evaluate the contribution of the soft mode to the out-of-time-order correlator up to order $\mathcal{O}(g^4)$. We show that the quantum correction of order $\mathcal{O}(g^4)$ by the soft mode decreases the maximum Lyapunov exponent $2π/ β$.
In this paper we provide a universal description of the behavior of the basic operators of the Schwarzian theory in pure states. When the pure states are energy eigenstates, expectation values of non-extensive operators are thermal. On the other hand, in coherent pure states, these same operators can exhibit ergodic or non-ergodic behavior, which is characterized by elliptic, parabolic or hyperbolic monodromy of an auxiliary equation; or equivalently, which coadjoint Virasoro orbit the state lies on. These results allow us to establish an extended version of the eigenstate thermalization hypot…
In this article, we explicitly demonstrate that, for a sufficiently generic class of examples, an open string embedded in an AdS-background yields an effective Schwarzian action and, in the semi-classical description, the fluctuation modes of the open string couple to this Schwarzian sector. This leads to a maximal chaos, observed in the open string degrees of freedom, irrespective of the gravitational background. This corresponds to the dynamics of quark-like degrees of freedom in a strongly coupled large N_c gauge theory. We also demonstrate a maximal chaos, resulting from an inherent D-bran…
We study the boundary effective action of the colored version of the Jackiw-Teitelboim (JT) gravity. We derive the boundary action, which is the color generalization of the Schwarzian action, from the $su(N,N)$ BF formulation of the colored JT gravity. Using different types of the $SU(N,N)$ group decompositions both the zero and finite temperature cases are elaborated. We provide the semi-classical perturbative analysis of the boundary action and discuss the instability of the spin-1 mode and its implication for the quantum chaos. A rainbow-AdS$_2$ geometry is introduced where the color gauge …
We study small instanton (and brane recombination) phase transitions in phenomenological models built with D-branes. By explicitly describing the cosmological dynamics of the moduli and matter fields, we show that these transitions do not occur smoothly, but are typically chaotic with the gauge group of the low energy theory fluctuating in time. We comment on the potential implications for cosmological questions such as inflation.
We study, by using tools of the dynamical system theory, a fermionic string streched from a non-commutative D2-brane (stack of D0-branes in the BFSS model) to a probe D0-brane as a quantum system driven by a chaotic system, the (classical and quantum) chaos being induced in the D2-brane dynamics by quantum fluctuations. We show that this dynamics with fluctuations induces a decoherence phenomenon on the reduced density matrix of the fermionic string which is characteristic of the chaotic behaviour since it presents an horizon of coherence. Moreover we show that this dynamics is associated with…
We use the wave-function method developed in area of quantum information to investigate the quantum circuit complexity of the small quantum fluctuations around the probe $D_3$ brane moving in $AdS_5\times S^5$ bulk. In our consideration, the reference and target states are chosen as the vacuum state and the squeezed quantum state respectively. The evolution of parameters characterizing the squeezed quantum state are governed by the time-dependent $Schr\ddot{o}dinger$ equation, in which the Hamiltonian operator is derived from the perturbative action of $D_3$ brane. For a quantum chaotic system…
We study a class of SYK-type models in large N limit from the gravity dual side in terms of Schwarzian action analytically. The quantum correction to two point correlation function due to the Schwarzian action produces transfer of degree of freedom from the quasiparticle peak to Hubbard band in density of states (DOS), a signature strong correlation. In Schwinger-Keldysh (SK) formalism, we calculate higher point thermal out-of-time order correlation (OTOC) functions, which indicate quantum chaos by having Lyapunov exponent. Higher order local spin-spin correlations are also calculated, which c…
We discuss $SL(N,\mathbb{C})$ Chern-Simons higher spin gauge theories in Euclidean AdS$_3$. 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 $\mathcal{W}$-Ward identity 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 …
We find an effective action for gravitational interactions with scalars in $AdS_3$ to first order in $G_N$ at the conformal boundary. This action can be understood as an action for the Brown-Henneaux modes and is given by the square-root product of right and left moving Schwarzian derivatives for conformal transformations of the boundary. We thus reproduce the result $λ_L=\frac{2π}β$ for OTOC computed first in arXiv:1412.6087 for a Schwarzchild black hole in $AdS_3$. Applying the same procedure to rotating BTZ we find the Lyapunov index to be $λ_L=\frac{2π}{β_+}>\frac{2π}β$ where $β_+=β(1-μ_L)…
We discuss the asymptotic dynamical evolution of spatially homogeneous brane-world cosmological models close to the initial singularity. We find that generically the cosmological singularity is isotropic in Bianchi type IX brane-world models and consequently these models do not exhibit Mixmaster or chaotic-like behaviour close to the initial singularity. We argue that this is typical of more general cosmological models in the brane-world scenario. In particular, we show that an isotropic singularity is a past-attractor in all orthogonal Bianchi models and is a local past-attractor in a class o…
By fast Lyapunov indicator (FLI), we study the chaotic dynamics of closed string around charged black brane with hyperscaling violation (HV). The Hawking temperature, Lifshitz dynamical exponent and HV exponent together affect the chaotic dynamics of this system. The temperature plays the role of driving the closed string to escape to infinity. There is a threshold value $z_{\ast}=2$, below which the string is captured by the black brane no matter where the string is placed at the beginning. However, when $z>2$, the string escapes to infinity if it is placed near the black brane at the beginni…
We continue the investigation of coupled Sachdev-Ye-Kitaev(SYK) models without Schwarzian action dominance. Like the original SYK, at large N and low energies these models have an approximate reparametrization symmetry. However, the dominant action for reparametrizations is non-local due to the presence of irrelevant local operator with small conformal dimension. We semi-analytically study different thermodynamic properties and the 4-point function and demonstrate that they significantly differ from the Schwarzian prediction. However, the residual entropy and maximal chaos exponent are the sam…
The early time behaviour of brane-world models is analysed in the presence of anisotropic stresses. It is shown that that the initial singularity cannot be isotropic, unless there is also an isotropic fluid stiffer than radiation present. Also, a magnetic Bianchi type I brane-world is analysed in detail. It is known that the Einstein equations for the magnetic Bianchi type I models are in general oscillatory and are believed to be chaotic, but in the brane-world model this chaotic behaviour does not seem to be possible.
We study chaos in the classical limit of the matrix quantum mechanical system describing D0-brane dynamics. We determine a precise value of the largest Lyapunov exponent, and, with less precision, calculate the entire spectrum of Lyapunov exponents. We verify that these approach a smooth limit as $N \rightarrow \infty$. We show that a classical analog of scrambling occurs with fast scrambling scaling, $t_* \sim \log S$. These results confirm the k-locality property of matrix mechanics discussed by Sekino and Susskind.
We analyze string-theoretic large-field inflation in the regime of spontaneously-broken supergravity with conventional moduli stabilization by fluxes and non-perturbative effects. The main ingredient is a shift-symmetric Kahler potential, supplemented by flux-induced shift symmetry breaking in the superpotential. The central technical observation is that all these features are present for D7-brane position moduli in Type IIB orientifolds, allowing for a realization of the axion monodromy proposal in a controlled string theory compactification. On the one hand, in the large complex structure re…
We classify and study defects in 2d Jackiw-Teitelboim gravity. We show these are holographically described by a deformation of the Schwarzian theory where the reparametrization mode is integrated over different coadjoint orbits of the Virasoro group. We show that the quantization of each coadjoint orbit is connected to 2d Liouville CFT between branes with insertions of Verlinde loop operators. We also propose an interpretation for the exceptional orbits. We use this perspective to solve these deformations of the Schwarzian theory, computing their partition function and correlators. In the proc…
We use holographic methods to study several chaotic properties of a super Yang-Mills theory at temperature $T$ in the presence of a background magnetic field of constant strength $\mathcal{B}$. The field theory we work on has a renormalization flow between a fixed point in the ultraviolet and another in the infrared, occurring in such a way that the energy at which the crossover takes place is a monotonically increasing function of the dimensionless ratio $\mathcal{B}/T^2$. By considering shock waves in the bulk of the dual gravitational theory, and varying $\mathcal{B}/T^2$, we study how seve…
Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question ---especially aspects of this question such as a black hole's negative specific heat---we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large $N$ limit. Simple arguments show that the b…
In the current manuscript we perform a systematic investigation about the effects of nonlocal interaction to the spread of quantum information in many body system. In particular, we have studied how nonlocality influence the existing bound on the growth rate of the commutator involving two local operators, the butterfly velocity. For this purpose, we consider the nonlocal theory on the worldvolume of $N\gg 1$, NS$5$ branes arising in the limit of vanishing string coupling, the `little string theory'. A direct evidence of nonlocality can be realized from the `volume law' behavior for the most d…
We study possible string theory compactifications which, in the low-energy limit, describe chaotic inflation with a stabilizer field. We first analyze type IIA setups where the inflationary potential arises from a D6-brane wrapping an internal three-cycle, and where the stabilizer field is either an open-string or bulk Kähler modulus. We find that after integrating out the relevant closed-string moduli consistently, tachyonic directions arise during inflation which cannot be lifted. This is ultimately due to the shift symmetries of the type IIA Kähler potential at large compactification volume…
In the present work warm inflationary universe model with viscous pressure on the brane in high-dissipation regime is studied. We derive a condition which is required for this model to be realizable in slow-roll approximation. We also present analytic expressions for density perturbation and amplitude of tensor perturbation in longitudinal gauge. General expressions of tensor-to-scalar ratio, scalar spectral index and its running are obtained. We develop our model by using chaotic potential, the characteristics of this model are calculated for two specific cases: 1- Dissipative parameter $Γ$ a…
We propose new large field inflation scenarios built on the framework of F-term axion monodromy. Our setup is based on string compactifications where D-branes create potentials for closed string axions via F-terms. Because the source of the axion potential is different from the standard sources of moduli stabilisation, it is possible to lower the inflaton mass as compared to other massive scalars. We discuss a particular class of models based on type IIA flux compactifications with D6-branes. In the small field regime they describe supergravity models of quadratic chaotic inflation with a stab…
We develop new scenarios of large field inflation in type IIA string compactifications in which the key ingredient is a D6-brane that creates a potential for a B-field axion. The potential has the multi-branched structure typical of F-term axion monodromy models and, near its supersymmetric minima, it is described by a 4d supergravity model of chaotic inflation with a stabiliser field. The same statement applies to the D6-brane Wilson line, which can also be considered as an inflaton candidate. We analyse both cases in the context of type IIA moduli stabilisation, finding an effective potentia…
Melnikov's method is an analytical way to show the existence of classical chaos generated by a Smale horseshoe. It is a powerful technique, though its applicability is somewhat limited. In this paper, we present a solution of type IIB supergravity to which Melnikov's method is applicable. This is a brane-wave type deformation of the AdS$_5\times$S$^5$ background. By employing two reduction ansätze, we study two types of coupled pendulum-oscillator systems. Then the Melnikov function is computed for each of the systems by following the standard way of Holmes and Marsden and the existence of cha…
Brane-like vertex operators, defining backgrounds with the ghost-matter mixing in NSR superstring theory, play an important role in a world-sheet formulation of D-branes and M theory, being creation operators for extended objects in the second quantized formalism. In this paper we show that dilaton's beta function in ghost-matter mixing backgrounds becomes stochastic. The renormalization group (RG) equations in ghost-matter mixing backgrounds lead to non-Markovian Fokker-Planck equations which solutions describe superstrings in curved space-times with brane-like metrics.We show that Feigenbaum…
We propose that inflation is driven by a (complex) neutral Higgs of the MSSM extension of the SM, in a chaotic-like inflation setting. The SUSY breaking soft term masses are of order $10^{12}-10^{13}$ GeV, which is identified with the inflaton mass scale and is just enough to stabilise the SM Higgs potential. The fine-tuned SM Higgs has then a mass around 126 GeV, in agreement with LHC results. We point out that the required large field excursions of chaotic inflation may be realised in string theory with the (complex) inflaton/Higgs identified with a continuous Wilson line or D-brane position…
