arXiv subjects

Amin Faraji Astaneh

Publications and source records attributed to Amin Faraji Astaneh.

At least 19 recordsLinked to original sources

arXiv2026

Freezing Swampland: A Krylov Complexity Criterion for the Weak Gravity Conjecture

We propose a quantum-information-theoretic perspective on the Weak Gravity Conjecture through the behavior of Krylov spread complexity. For a charged thermofield double state holographically dual to an AdS Reissner--Nordström black hole, we show that the extremal limit on the black-hole side is accompanied by an effective freezing of Krylov spreading. In this regime, the return amplitude becomes effectively a pure phase, and the dual quantum state ceases to spread nontrivially in Krylov space. We then incorporate charged matter and study the effect of Schwinger pair production in the near-horizon region. Within this semiclassical near-extremal analysis, the frozen behavior is lifted once the discharge channel is opened, and the dynamics become nontrivial again. This suggests that the Weak Gravity Conjecture may admit a complexity-based interpretation in terms of the absence of exact freezing in the presence of an available discharge channel. More broadly, our results point to a new connection between the swampland program, black-hole physics, and quantum information theory.

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arXiv2026

Krylov Complexity for Time-Dependent Hamiltonians

We investigate Krylov spread complexity for states evolving under time-dependent Hamiltonians. For periodically driven systems, we formulate the problem within Floquet theory and show how the Magnus expansion provides a systematic approximation when the Floquet Hamiltonian is not available in closed form. We then extend this framework beyond periodic driving and demonstrate that, in addition to the globally truncated Magnus expansion, a piecewise Magnus expansion provides a reliable method when the global expansion loses convergence or accuracy. Our results provide practical tools for analyzing complexity growth in a broad class of time-dependent quantum systems.

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arXiv2025

Generalized Krylov Complexity

We extend the concept of Krylov complexity to include general unitary evolutions involving multiple generators. This generalization enables us to formulate a framework for generalized Krylov complexity, which serves as a measure of the complexity of states associated with continuous symmetries within a model. Furthermore, we investigate scenarios where different directions of transformation lead to varying degrees of complexity, which can be compared to geometric approaches to understanding complexity, such as Nielsen complexity. In this context, we introduce a generalized orthogonalization algorithm and delineate its computational framework, which is structured as a network of orthogonal blocks rather than a simple linear chain. Additionally, we provide explicit evaluations of specific illustrative examples to demonstrate the practical application of this framework.

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arXiv2025

Average Spread Complexity and the Higher-Order Level Spacing

We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level spacing, we observe the characteristic slope-dip-ramp-plateau structure. Further investigation reveals that certain matrix models exhibit additional iterative peaks, motivating us to generalize the known spacing distributions to higher-order level spacings. While this structure persists in chaotic systems, we find that integrable systems can also display similar features, highlighting limitations in using complexity as a universal diagnostic of quantum chaos.

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arXiv2024

Boundary conformal invariants and the conformal anomaly in five dimensions

In odd dimensions the integrated conformal anomaly is entirely due to the boundary terms \cite{Solodukhin:2015eca}. In this paper we present a detailed analysis of the anomaly in five dimensions. We give the complete list of the boundary conformal invariants that exist in five dimensions. Additionally to 8 invariants known before we find a new conformal invariant that contains the derivatives of the extrinsic curvature along the boundary. Then, for a conformal scalar field satisfying either the Dirichlet or the conformal invariant Robin boundary conditions we use the available general results for the heat kernel coefficient $a_5$, compute the conformal anomaly and identify the corresponding values of all boundary conformal charges.

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arXiv2024

Quantum Complexity of $T\bar{T}$-deformation and Its Implications

We employ holography to calculate the quantum complexity of $T\bar{T}$-deformation, utilizing the complexity equals volume (CV) and the complexity equals action (CA) proposals within the bulk spacetime with a finite radius cutoff. We find that the complexity of the deformed theory differs from the renormalized complexity of the original theory by a geometric functional: the bending (Willmore) energy of the time-constant slice of the base manifold. We use this result to propose an unambiguous scheme for calculating holographic quantum complexity through the CA proposal.

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arXiv2024

Holographic Action Principle for $T\bar{T}$-deformation

We explore the action principle for the holographic $T\bar{T}$-deformation. We develop a scheme in which one can holographically reproduce the action of the Liouville theory deformed by $T\bar{T}$-insertion. This scheme necessitates considering the bending energy of the finite cut-off surface. Following our proposal, one observes a perfect match between the actions of deformed theory on the field theory and gravity sides.

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arXiv2023

Fermions, boundaries and conformal and chiral anomalies in $d=3,\ 4$ and $5$ dimensions

In the presence of boundaries, the quantum anomalies acquire additional boundary terms. In odd dimensions the integrated conformal anomaly, for which the bulk contribution is known to be absent, is non-trivial due to the boundary terms. These terms became a subject of active study in the recent years. In the present paper we continue our previous study [1], [2] and compute explicitly the anomaly for fermions in dimensions $d=3, \ 4 \ $ and $5$. The calculation in dimension $5$ is new. It contains both contributions of the gravitational field and the gauge fields to the anomaly. In dimensions $d=3$ and $4$ we reproduce and clarify the derivation of the results available in the literature. Imposing the conformal invariant mixed boundary conditions for fermions in odd dimension $d$ we particularly pay attention to the necessity of choosing the doubling representation for gamma matrices. In this representation there exists a possibility to define chirality and thus address the question of the chiral anomaly. The anomaly is entirely due to terms defined on the boundary. They are calculated in the present paper in dimensions $d=3$ and $5$ due to both gravitational and gauge fields. To complete the picture we re-evaluate the chiral anomaly in $d=4$ dimensions and find a new boundary term that is supplementary to the well-known Pontryagin term.

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arXiv2023

Energy of Decomposition and Entanglement Thermodynamics for $T^2$-deformation

We have presented a set of laws of entanglement thermodynamics for $T\bar{T}$-deformed CFTs and in general for $T^2$-deformed field theories. In particular, the first law of this set, states that although we are dealing with a non-trivial deformed theory, the change of the entanglement entropy is simply translated to the change of the bending energy of the entangling surface. We interpret this energy as the energy of decomposition. Probing the whole spectrum of the deformed theory, a second law also results, which suggests an inequality that the first law is derived from its saturation limit. We explain that this second law guarantees the preservation of the unitarity bound. The thermodynamical form of these laws requires us to define the temperature of deformation and express its characteristics, which is the subject of the third law. We use a holographic approach in this analysis and in each case, we consider the generalization to higher dimensions.

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arXiv2022

Aspects of Holographic Entanglement Entropy for $T\bar{T}$-deformed CFTs

We use the holographic methods to calculate the entanglement entropy for field theories modified by $T\bar{T}$ insertion. Based on the available holographic proposals, this calculation reduces to the holographic computations in AdS with finite cut-off. We perform a direct holographic calculation of the entanglement entropy for two dimensional deformed theory. By direct we mean the evaluation of the gravitational action in the bulk spacetime which has been reconstructed from a dual CFT$_2$ on $n$-sheeted Riemann surface as a finite cut-off boundary. We also apply Ryu-Takayanagi's prescription to investigate the most general structure of the entanglement entropy for $T\bar{T}$-deformed theories of arbitrary dimensions. In both cases, we find a perfect agreement with the known results.

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arXiv2021

Island in the Presence of Higher Derivative Terms

Using extended island formula we compute entanglement entropy of Hawking radiation for black hole solutions of certain gravitational models containing higher derivative terms. To be concrete we consider two different four dimensional models to compute entropy for both asymptotically flat and AdS black holes. One observes that the resultant entropy follows the Page curve, thanks to the contribution of the island, despite the fact that the corresponding gravitational models might be non-unitary.

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arXiv2021

On Free Energy for Deformed JT Gravity

In this paper, we study a particular deformation of the Jackiw-Teitelboim gravity recently considered by Maxfield, Turiaci and independently by Witten. We will compute the partition function of this model as well as its higher order correlators to all orders in genus expansion in the low temperature limit for small perturbations. In this limit, the results match with those obtained from the Airy limit of a Hermitian random matrix ensemble. Using this result, we will also study the free energy of the model. One observes that although the annealed free energy has pathological behaviors, under certain assumptions, the quenched free energy evaluated by replica trick exhibits the desired properties at low temperatures.

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arXiv2019

Complexity of Hyperscaling Violating Theories at Finite Cutoff

Using the complexity equals action proposal we study holographic complexity for hyperscaling violating theories in the presence of a finite cutoff that, in turns, requires to obtain all counter terms needed to have finite boundary energy momentum tensor. These terms could give non-trivial contributions to the complexity. We observe that having a finite UV cutoff would enforce us to have a cutoff behind the horizon whose value is fixed by the UV cutoff; moreover, certain counter term should be defined on the cutoff behind the horizon too.

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arXiv2018

Complexity Growth with Lifshitz Scaling and Hyperscaling Violation

Using complexity=action proposal we study the growth rate of holographic complexity for Lifshitz and hyperscaling violating geometries. We will consider both one and two sided black branes in an Einstein-Maxwell-Dilaton gravitational theory. We find that in either case Lloyd's bound is violated and the rate of growth of complexity saturates to a value which is greater than twice the mass of the corresponding black brane. This value reduces to the mass of the black brane in the isotropic case. We show that in two sided black brane the saturation happens from above while for one sided black brane it happens from below.

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arXiv2017

On Complexity for Higher Derivative Gravities

Using "complexity=action" proposal we study complexity growth of certain gravitational theories containing higher derivative terms. These include critical gravity in diverse dimensions. One observes that the complexity growth for neutral black holes saturates the proposed bound when the results are written in terms of physical quantities of the model. We will also study effects of shock wave to the complexity growth where we find that the presence of massive spin-2 mode slows down the rate of growth.

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arXiv2017

Holographic calculation of entanglement entropy in the presence of boundaries

When a spacetime has boundaries, the entangling surface does not have to be necessarily compact and it may have boundaries as well. Then there appear a new, boundary, contribution to the entanglement entropy due to the intersection of the entangling surface with the boundary of the spacetime. We study the boundary contribution to the logarithmic term in the entanglement entropy in dimensions $d=3$ and $d=4$ when the entangling surface is orthogonal to the boundary. In particular, we compute a boundary term in the entropy of ${\mathcal{N}}=4$ super-gauge multiplet at weak coupling. This result is compared with the holographic calculation of the entropy based on the Ryu-Takayanagi proposal adapted appropriately to the present situation. We find a complete agreement between these two calculations provided the boundary conditions imposed on the gauge multiplet preserve $1/2$ of the supersymmetry and the extension of the boundary into the AdS bulk is a minimal hypersurface.

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arXiv2017

Holographic Fidelity Susceptibility

For a field theory with a gravitational dual, we study holographic fidelity susceptibility for two states related by a deformation of a relevant operator. To do so, we study back reaction of a massive scalar field on the asymptotic behavior of the metric in an Einstein gravity coupled to a massive scalar field. Identifying the two states, holographically, with the original and back reacted geometries, the corresponding holographic fidelity susceptibility is given by the difference of the volume of an extremal time slice evaluated on the original and back reacted geometries.

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arXiv2017

Holographic calculation of boundary terms in conformal anomaly

In the presence of boundaries the integrated conformal anomaly is modified by the boundary terms so that the anomaly is non-vanishing in any (even or odd) dimension. The boundary terms are due to extrinsic curvature whose exact structure in $d=3$ and $d=4$ has recently been identified. In this note we present a holographic calculation of those terms in two different prescriptions for the holographic description of the boundary CFT. We stress the role of supersymmetry when discussing the holographic description of ${\cal N}=4$ SYM on a $4$-manifold with boundaries.

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