arXiv subjects

Mahdis Ghodrati

Publications and source records attributed to Mahdis Ghodrati.

At least 19 recordsLinked to original sources

arXiv2026

The spectral gap of the ABJM model: A holographic perspective from uplifted higher-dimensional geometries

We study the $U(1)^4$ charged black brane solution of four-dimensional gauged supergravity and analyze the fermionic response in this geometry, which is holographically dual to $3d$ $\mathcal{N}=2$ SCFT ABJM models. Similar to \cite{DeWolfe:2013fha}, we show that a gap exists in the states of the conformal field theory, which corresponds to the different limiting behaviors of the two unequal chemical potentials of the four-charge geometry. We study the behavior of this gap and also the stability of the near-horizon geometry by changing the parameters of the theory in various orders. We then categorize the $56$ fermion modes of the geometry, find the coefficients of the Dirac equations for each mode, and comment on the behavior of the solution of the Dirac equation in different near-horizon limits. We then uplift the geometry to five-dimensional and then to eleven-dimensional geometries and, similar to \cite{Fareghbal:2008dy}, we show that in both cases, a piece of $\mathrm{BTZ} \times \mathrm{S}^2$ or $\mathrm{AdS}^3 \times \mathbb{R}^2$ emerges, and as a result, a decoupling sector in the field theory exists. We study the singularity of the near-horizon $4d$ geometry and the mentioned gap in these uplifted geometries.

hep-th↗

arXiv2026

Modular Flow of Celestial Conformal Field Theory

We first review the calculations for the modular flow and the vector flow of $\text{CFT}_2$, warped CFTs and Bondi-Metzner-Sachs Field Theories (BMSFTs), and then we present the vector flows and modular flows in Celestial field theory and Klein CFTs. We also discuss the search for this structure in Lifshitz and other exotic field theories.

hep-th↗

arXiv2026

Some universalities in the partition functions of low-dimensional gravity models

In this work, first, we discuss the connections between various low-dimensional quantum gravity models, including 3d Chern-Simons, 2d JT, 2d BF theory, 2d Liouville, 2d WZW, and 1d Schwarzian, which are related through holography and dimension reduction, and discuss some universalities in their partition functions. Then, we specifically examine the JT partition function and the partition function of $\mathcal{N}=(2,2)$ on $S^2$ and $\text{AdS}_2$ and discuss their similarities and therefore examine our proposed universalities. We change the parameters in each model and based on the change in the structure of the partition functions, strengthen our conjectures. We also use eigenfunctions, spectra and the behaviors of Wheeler-DeWitt wavefunctions to generate more universalities between these low-dimensional quantum gravity models, specifically in their partition functions. Then, we use entanglement entropy, complexity and RG flows, particularly in the context of wormholes, to find more universalities in quantum gravity models. Finally, we use the new results about the connections between wormholes and defects to discuss our universalities further.

hep-th↗

arXiv2026

Black holes with quantum corrections in $3d$: The case of Page curve in Lindblad, greybody factor, and Lyapunov exponent

In this work, first we discuss black holes with quantum corrections as an open quantum system and apply Lindblad formalism to explain the ``zig-zag" behavior in the Hawking- Page curve and radiation process, specially by considering the effects of exceptional points. Then, we calculate quantum corrections for various parameters of $3d$ Cotler-Jensen theory which is $\text{AdS}_3$ with reparametrized modes. At each step of the calculations, we compare the results with the case of JT. We then calculate quantum-corrected greybody factor for various black hole solutions, and specially for the case of Cotler-Jensen theory. Finally, we study the effects of quantum corrections on Lyapunov exponent, potential, and quantum information structure of black holes.

hep-th↗

arXiv2026

Photonic Exceptional Points in Holography and QCD

In this work, based on an analogy with holographic confining geometries and using complexified fields, we build a holographic toy model of third order photonic exceptional points (EPs) of ternary coupled microrings with gain and loss, which makes an open, non-Hermitian quantum system. In our model, we discuss the Ferrell-Glover-Tinkham sum rule for various combinations of gain and loss systems, and numerically find the behavior of spectra which matches with the experiments. We also discuss the inhomogeneous case of a holographic lattice for three-site photonic EPs. Additionally, we numerically find the behavior of phase rigidity and the Petermann factor around EPs versus various parameters of the model. We also discuss the connections between recent developments in complexified, time-dependent entanglement entropy and EPs, and then, we connect EPs and the $θ$-vacuum of QCD through topological structures, partition functions, and winding numbers, and find a second-order EP in a perturbed $θ$-vacuum model. Finally, we examined a controlled non-Hermitian deformation of $θ$-vacuum toy model, by using the Lindblad formalism and Liouvillian eigenvalues.

hep-th↗

arXiv2025

String amplitudes and mutual information in confining backgrounds: the partonic behavior

In the background of several holographic confining backgrounds, we present the connections between the behaviors of string scattering amplitudes and mutual information. We lay down the analogies between the logarithmic branch cut behavior of the string scattering amplitude in $4d$, $ \mathcal{A}_4 $, at low and medium Mandelstam variable $s$ observed in \cite{Bianchi:2021sug}, which is due to the dependence of the string tension on the holographic coordinate, and the branch cut behavior observed in mutual information and critical distance $D_c$ at low-cut-off variable $u_{KK}$ studied in our previous work \cite{Ghodrati:2021ozc}. It can also be seen that in both cases, as $s$ or $u_{KK}$ increases, the peaks in the branch cuts fade away in the form of $\text{Re}\lbrack \mathcal{A}_4 \rbrack \propto s^{-1}$. Then, we used modular flow and modular Hamiltonian as intermediary concept to further clarify the observed connection. We discussed how mutual information itself can detect chaos in various scenarios. In addition, we considered two examples of Compton scattering between two photons and also the decay of a highly excited string into two tachyons and scrutinized the pattern of entanglement entropy and the change in the mutual information in these examples. Then, the kink-kink and kink-antikink scatterings as simple models of scattering in confining geometries have been used to examine the fractal structures in the scatterings of topological defects. Finally, the relationships between Regge conformal block and quantum error correction codes through pole-skipping and chaos bound have been postulated. These observed connections can further establish the ER$=$EPR conjecture and the general interdependence between the scattering amplitudes and entanglement entropy.

hep-th↗

arXiv2023

Encoded information of mixed correlations: the views from one dimension higher

After reviewing the JT gravity, we discuss the four saddles in the mixed correlation measures of black holes Hawking radiation in the setup of geometric evaporation of \cite{Verheijden:2021yrb}. By looking from $1d$ higher point of view and partial dimensional reduction, we examine the phase structures and the universalities for these four saddles. We also discuss the behavior of quantum error correction codes for each of these four phases, reaching to consistent results. Then, instead of dimension reduction between Einstein gravity and JT, we try to explore the connections between partition functions and saddles of $3d$ Chern-Simons and $2d$ BF theories, $2d$ Liouville and $2d$ Wess-Zumino-Witten models, and also the dimensionally reduced $1d$ Schwarzian and $1d$ particles on group. We specifically sketch on the connections between these theories in the setup of mixed correlations and island formulation.

hep-th↗

arXiv2023

Chaos, Phase Transitions and Curvature Invariants of (rotating, warped, massive) BTZ Black Holes

Combining several results from the previous works of the author, three main subtleties will be clarified here. First, similar to the rotating BTZ black holes, we show how for the warped BTZ black holes, the consideration of the effective temperatures could solve the seemingly unsaturation issue of the chaos bound. Second, comparing the Hawking-Page phase diagrams of BTZ and warped BTZ black holes in the topologically massive gravity and new massive gravity theories, we show how the characteristics of the action would specify the behaviors of the chaos modes, and there we emphasize the importance of using the local and "physical" thermodynamical ensembles for studying the boundary chaos modes in warped CFTs and also the connections with the bulk reconstruction. Third, we propose that the boundary modular scrambling modes which saturate the modular chaos bound are related to the curvature invariants in the geometrical side.

hep-th↗

arXiv2023

On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli Black Holes and Their Holographic Pictures

In this paper, the curvature structure of a (2+1)-dimensional black hole in the massive-charged-Born-Infeld gravity is investigated. The metric that we consider is characterized by four degrees of freedom which are the mass and electric charge of the black hole, the mass of the graviton field, and a cosmological constant. For the charged and neutral cases separately, we present various constraints among scalar polynomial curvature invariants which could invariantly characterize our desired spacetimes. Specially, an appropriate scalar polynomial curvature invariant and a Cartan curvature invariant which together could detect the black hole horizon would be explicitly constructed. Using algorithms related to the focusing properties of a bundle of light rays on the horizon which are accounted for by the Raychaudhuri equation, a procedure for isolating the black hole parameters, as the algebraic combinations involving the curvature invariants, would be presented. It will be shown that this technique could specially be applied for black holes with zero electric charge, contrary to the cases of solutions of lower-dimensional non-massive gravity. In addition, for the case of massive (2+1)-dimensional black hole, the irreducible mass, which quantifies the maximum amount of energy which could be extracted from a black hole would be derived. Therefore, we show that the Hawking temperatures of these black holes could be reduced to the pure curvature properties of the spacetimes. Finally, we comment on the relationship between our analysis and the novel roles it could play in numerical quark-gluon plasma simulations and other QCD models and also black hole information paradox where the holographic correspondence could be exploited.

hep-th↗

arXiv2022

Critical distance and Crofton form in confining geometries

For two symmetric strips with equal and finite size and in the background of several confining geometries, we numerically calculate the critical distance between these two mixed systems where the mutual information between them drops to zero and show that this quantity could be a useful correlation measure in probing the phase structures of holographic QCD models. The models that we consider here are Sakai-Sugimoto and deformed Sakai-Sugimoto, Klebanov-Tseytlin and Maldacena Nunez. For evaluating the structures of these holographic supergravity geometries from the perspective of the bulk reconstruction, we also calculate their Crofton forms and show that there is a universal behavior in the confining backgrounds where a "well functionality" is present around the IR cutoff point, and far from the IR wall the scalar part of the Crofton form would become constant, demonstrating the effects of the wall of the confining models on the phase structures. This work is the shorter version of our previous work arXiv:2110.12970 with few more results about the connections between phases.

hep-th↗

arXiv2022

Correlations of mixed systems in confining backgrounds

We show that the entanglement of purification and the critical distance between the two mixed systems is a powerful measure in probing the phase structures of QCD and confining backgrounds, as it can distinguish the scale of chiral symmetry breaking versus the scale of confinement/deconfinement phase transitions. For two symmetric strips with equal and finite width and infinite length, and in the background of several confining geometries, we numerically calculate the critical distance between them where the mutual information vanishes and show that this quantity can probe the very rich phase structures of these backgrounds. The geometries that we study here are AdS-soliton, Witten Sakai Sugimoto and deformed Sakai-Sugimoto, Witten-QCD, Klebanov-Strassler, Klebanov-Tseytlin, Klebanov-Witten, Maldacena-Nunez, Nunez-Legramandi metric, and Domain-Wall QCD model. For each background we also present the relation for the entanglement of purification. Finally, we show that the Crofton forms of these geometries also behave in a universal form where a "well" is being observed around the IR wall, and therefore for all confining backgrounds, the Crofton form would also be capable of distinguishing the confining versus conformal backgrounds as it is also a tool in the reconstruction of various bulk geometries.

hep-th↗

arXiv2021

Entanglement wedge reconstruction and correlation measures in mixed states: modular flows versus quantum recovery channels

In this work we study the nature of correlations among mixed states in the setup of two symmetric strips. We use various tools to determine how the bulk geometry could be reconstructed from the boundary mixed information. These tools would be the modular Hamiltonian and modular flow, OPE blocks, quantum recovery channels such as Petz map, Uhlmann holonomy and Wilson lines. We comment on the similarities and connections between these approaches in our symmetric setup of a mixed system. Specially, we use parameters such as dissipation which is being modeled by the mass of graviton, and also the same sign charge of the two strips to find connections between these different approaches. Then, using Uhlmann fidelity as the correlation measure, we look into the various types of correlations in mixed systems such as discord. Next, we use simple results of modular Hamiltonian for fermions to get insights about the relations between modular flow and entanglement and complexity of purification (EoP/CoP), and also behavior of modular flows in confining geometries. Finally, we study the dynamics of correlations using various information speeds and also model of void formation in CFTs and again we comment on their relationships with the behavior of EoP and CoP.

hep-th↗

arXiv2019

Complexity and Emergence of Warped $\text{AdS}_3$ Space-time from Chiral Liouville Action

In this work we explore the complexity path integral optimization process for the case of warped $\text{AdS}_3$/warped $\text{CFT}_2$ correspondence. We first present the specific renormalization flow equations and analyze the differences with the case of CFT. We discuss how the "chiral Liouville action" could replace the Liouville action as the suitable cost function for this case. Starting from the other side of the story, we also show how the deformed Liouville actions could be derived from the spacelike, timelike and null warped metrics and how the behaviors of boundary topological terms creating these metrics, versus the deformation parameter are consistent with our expectations. As the main results of this work, we develop many holographic tools for the case of warped $\text{AdS}_3$, which include the tensor network structure for the chiral warped CFTs, entangler function, surface/state correspondence, quantum circuits of Kac-Moody algebra and kinematic space of WAdS/WCFTs. In addition, we discuss how and why the path-integral complexity should be generalized and propose several other examples such as Polyakov, p-adic strings and Zabrodin actions as the more suitable cost functions to calculate the circuit complexity.

hep-th↗

arXiv2019

The connection between holographic entanglement and complexity of purification

In this work we study how entanglement of purification (EoP) and the new quantity of "complexity of purification" are related to each other using the $E_P=E_W$ conjecture. First, we consider two strips in the same side of a boundary and study the relationships between the entanglement of purification of this mixed state and the parameters of the system such as dimension, temperature, length of the strips and the distance between them. Next, using the same setup, we introduce two definitions for the complexity of mixed states, complexity of purification (CoP) and the interval volume (VI). We study their connections to other parameters similar to the EoP case. Then, we extend our study to more general examples of BTZ black holes solution in massive gravity, charged black holes and multipartite systems. Finally, we give various interpretations of our results using resource theories such as LOCC and also bit thread picture.

hep-th↗

arXiv2019

Evolutions of entanglement and complexity after a thermal quench in massive gravity theory

We study the evolution of the holographic entanglement entropy (HEE) and the holographic complexity (HC) after a thermal quench in $1+1$ dimensional boundary CFTs dual to massive BTZ black holes. The study indicates how the graviton mass $m_g$, the charge $q$, and also the size of the boundary region $l$ determine the evolution of the HEE and HC. We find that for small $q$ and $l$, the evolutions of the HEE and the HC is a continuous function. When $q$ or $l$ is tuned larger, the discontinuity emerges, which could not observed in the neutral AdS$_3$ backgrounds. We show that, the emergence of this discontinuity is a universal behavior in the charged massive BTZ theory. With the increase of graviton mass, on the other hand, no emergence of the discontinuity behavior for any small $q$ and $l$ could be observed. We also show that the evolution of the HEE and HC both become stable at later times, and $m_g$ speeds up reaching to the stability during the evolution of the system. Moreover, we show that $m_g$ decreases the final stable value of HEE but raises the stable value of HC. Additionally, contrary to the usual picture in the literature that the evolution of HC has only one peak, for big enough widths, we show that graviton mass could introduce two peaks during the evolution. However, for large enough charges the one peak behavior will be recovered again. We also examine the evolutions of HEE and HC growths at the early stage, which an almost linear behavior has been detected.

hep-th↗

arXiv2018

Complexity growth rate during phase transitions

We present evidences for the connection between the potential of different fields and complexity growth rates both in conformal and confining cases. By studying different models, we also establish a strong connection between phase transitions and the discontinuities in the complexity growth rates. In the first example, for the dyonic black holes which are dual to van der Waals fluids, we find a similar first order phase transition in the behavior of complexity growth rate. We then compare the Schwinger effect and also the behavior of complexity in the AdS and AdS soliton backgrounds and comment on the connection between them. Finally, in a general Gubser model of QCD, we present the connections between the potentials, entropies, speed of sounds and complexity growth rates during crossover, first and second order phase transitions and also the behavior of quasinormal modes.

hep-th↗

arXiv2017

On complexity growth in massive gravity theories, the effects of chirality and more

To study the effect of parity-violation on the rate of complexity growth, by using "Complexity=Action" conjecture, we find the complexity growth rates in different solutions of the chiral theory of Topologically Massive Gravity (TMG) and parity-preserving theory of New Massive Gravity (NMG). Using the results, one can see that decreasing the parameter $μ$, which increases the effect of Chern-Simons term and increases chirality, would increase the rate of growth of complexity. Also one can observe a stronger correlation between complexity growth and temperature rather than complexity growth and entropy. At the end we comment on the possible meaning of the deforming term of chiral Liouville action for the rate of complexity growth of warped CFTs in the Tensor Network Renormalization picture.

hep-th↗

arXiv2017

Phase transitions in Bergshoeff-Hohm-Townsend Massive Gravity

We present the Hawking-Page phase diagrams in the Bergshoeff-Hohm-Townsend (BHT) massive gravity theory for different solutions, such as the phase transitions between vacuum $\text{AdS}_3$ and BTZ black hole, warped $\text{AdS}_3$ and warped BTZ black hole in grand canonical and in non-local/quadratic ensembles, Lifshitz black hole and the new hairy black hole solutions. We observe that except for the black holes in quadratic ensemble, for other cases in the non-chiral theory of BHT the phase diagrams are symmetric with respect to the direction of angular momentum, as we expected. We conclude that for presenting the phase diagrams of warped $\text{AdS}_3$ black holes, only the grand canonical ensemble should be used.

hep-th↗