arXiv subjects

Mostafa Ghasemi

Publications and source records attributed to Mostafa Ghasemi.

10 recordsLinked to original sources

arXiv2026

Defect relative entropy in symmetric orbifold CFTs

In this work, we compute the defect relative entropy between topological defects in the symmetric product orbifold CFT $\mathrm{Sym}^N(M) = M^{\otimes N}/S_N$. Our analysis covers two distinct classes of defects: universal defects, which realize the $\mathrm{Rep}(S_N)$ non-invertible symmetry, and non-universal defects. We show that the defect relative entropy reduces to a Kullback--Leibler (KL) divergence. The resulting expression decomposes naturally into two contributions: one governed by characters of the symmetric group $S_N$, and the other controlled by modular $S$-matrix elements of the seed RCFT. Remarkably, both sets of data appear as probability distributions, yielding an information-theoretic interpretation of permutation group data and modular data within the symmetric orbifold. The structure of the divergence depends sensitively on the defect class. For universal defects, only the permutation group data contributes; for maximally fractional defects, both permutation and modular data enter and together define the relevant probability distributions. This feature suggests that the maximally fractional defect can be understood as a kind of product of the RCFT defect and the symmetric orbifold defect.

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arXiv2026

Defect Relative Entropy

Distinguishability is central to quantum information theory, but a quantitative measure for distinguishing topological defects--realizations of generalized symmetries in quantum field theory (QFT)--has been lacking. We introduce the notion of the \textit{defect relative entropy} to fill this gap for topological defects in two-dimensional conformal field theories (CFTs). For defects on a circle, we derive a universal formula that reduces defect relative entropy to a Kullback--Leibler divergence determined entirely by the modular $\mathcal{S}$-matrix and defect coefficients. Thus, the algebraic data governing modular transformations also determines defect distinguishability. A striking consequence is that certain distinct defects can have vanishing relative entropy when restricted to one side, implying that an observer confined to that side cannot distinguish them. This gives rise to information-theoretic equivalence classes of defects, which we term \textit{defect relative sectors}. We further introduce the sandwiched defect R\'enyi relative entropy and defect fidelity, derive general formulas for these quantities. Explicit calculations in the Ising model, tricritical Ising model, and $\widehat{su}(2)_k$ WZW models illustrate our results.

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arXiv2024

Left-Right Relative Entropy

The concept of distinguishability lies at the heart of quantum information theory. We introduce \textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional conformal field theories (CFTs). By tracing over either the left- or right-moving modes, we derive a universal formula for arbitrary regularized boundary states defined on a circle. Remarkably, the resulting quantity reduces to a Kullback--Leibler divergence, where the associated probability distribution is determined entirely by the modular $\mathcal{S}$-matrix and the boundary data. For diagonal CFTs, we obtain exact expressions for the left-right relative entropy in terms of modular data, and extend the framework to define \textit{Sandwiched Left-Right R\'enyi relative entropies} and \textit{left-right fidelity}. Applying this formalism to the Ising model, tricritical Ising model, and $\widehat{su}(2)_k$ WZW model, we uncover a striking phenomenon: the left-right relative entropy between certain reduced boundary states vanishes even though the corresponding global boundary states are orthogonal. This observation motivates the introduction of \textit{relative entanglement sectors}, defined as equivalence classes of boundary states that are indistinguishable with respect to left-right relative entropy. These sectors transform as NIM-representations of global symmetries and exhibit level-dependent structures that mirror $\mathbb{Z}_2$ 't Hooft anomalies. Our findings establish an unexpected bridge between quantum information measures, boundary conformal symmetry, and quantum anomaly constraints.

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arXiv2024

Symmetry-Resolved Relative Entropy of Random States

We use large-$N$ diagrammatic techniques to calculate the relative entropy of symmetric random states drawn from the Wishart ensemble. These methods are specifically designed for symmetric sectors, allowing us to determine the relative entropy for random states exhibiting $U(1)$ symmetry. This calculation serves as a measure of distinguishability within the symmetry sectors of random states. Our findings reveal that the symmetry-resolved relative entropy of random pure states displays universal statistical behavior. Furthermore, we derive the symmetry-resolved Page curve. These results deepen our understanding of the properties of these random states.

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arXiv2022

Universal Thermal Corrections to Symmetry-Resolved Entanglement Entropy and Full Counting Statistics

We consider the symmetry-resolved R\'{e}nyi and entanglement entropies for two-dimensional conformal field theories on a circle at nonzero temperature. We assume a unique ground state with a nonzero mass gap induced by the system's finite size and then calculate the leading corrections to the contributions of individual charge sectors in a low-temperature expansion. Besides the size of the mass gap and the degeneracy of the first excited state, these universal corrections depend only on the four-point correlation function of the primary fields. We also obtain thermal corrections to the full counting statistics of the ground state and define the \textit{probability fluctuations} function. It scales as $e^{-2 \pi \Delta_{\psi} \beta /L}$, where $\Delta_{\psi}$ is the scaling dimension of the lowest weight states. As an example, we explicitly evaluate the thermal corrections to the symmetry-resolved entanglement entropy and FCS for the spinless fermions.

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arXiv2021

Odd Entanglement Entropy and Logarithmic Negativity for Thermofield Double States

We investigate the time evolution of odd entanglement entropy (OEE) and logarithmic negativity (LN) for the thermofield double (TFD) states in free scalar quantum field theories using the covariance matrix approach. To have mixed states, we choose non-complementary subsystems, either adjacent or disjoint intervals on each side of the TFD. We find that the time evolution pattern of OEE is a linear growth followed by saturation. On a circular lattice, for longer times the finite size effect demonstrates itself as oscillatory behavior. In the limit of vanishing mass, for a subsystem containing a single degree of freedom on each side of the TFD, we analytically find the effect of zero-mode on the time evolution of OEE which leads to logarithmic growth in the intermediate times. Moreover, for adjacent intervals we find that the LN is zero for times $t < \beta/2$ (half of the inverse temperature) and after that, it begins to grow linearly. For disjoint intervals at fixed temperature, the vanishing of LN is observed for times $t<d/2$ (half of the distance between intervals). We also find a similar delay to see linear growth of $\Delta S=S_{\text{OEE}}-S_{\text{EE}}$. All these results show that the dynamics of these measures are consistent with the quasi-particle picture, of course apart from the logarithmic growth.

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arXiv2019

Constraints on anisotropic RG flows from holographic entanglement entropy

In the context of the gauge/gravity duality, using the proposed candidate $c$-function, which is derived from the entanglement entropy of a strip-shaped region, we investigate the RG flow for $d+1$-dimensional quantum field theories with broken Lorentz and rotational symmetries in the IR, but preserved conformal invariance in the UV boundary. We examine conditions of monotonicity of the $c$-function for holographic anisotropic theories dual to the Einstein gravity via the constraints imposed by the null energy conditions. We consider near UV and IR behaviors and identify the sufficient conditions that guarantee the $c$ function decreases monotonically along the RG flows.

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arXiv2019

Curved Corner Contribution to the Entanglement Entropy in an Anisotropic Spacetime

In this article, we explore the divergences and universal terms of the holographic entanglement entropy for singular regions in anisotropic and nonconformal theories that are holographically dual to geometries with a hyperscaling violation, parameterized by two parameters $z$ and $\theta$. We study a curved corner in anisotropic space with arbitrary $\theta$ and $z$. We choose the region to be shape invariant under the scaling of spacetime. For this case, we show that the contribution of the singularity to the entanglement entropy depends on $z$ and $\theta$ values. We identify the structure of various divergences that may appear, especially those which give rise to a universal contribution in the form of logarithmic or double logarithmic terms. In the range $z>1$, for values $z=2k/(2k-1)$ with some integer $k$ and $\theta=0$, Lifshitz geometry, we find a double logarithmic term. In the range $z<0$, for values $\theta=1-2n|z-1|$ with some integer $n$ we find a logarithmic term.

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arXiv2019

Relevant perturbation of entanglement entropy of singular surfaces

We study the entanglement entropy of theories that are derived from relevant perturbation of given CFTs for regions with a singular boundary by using the AdS/CFT correspondence. In the smooth case, it is well known that a relevant deformation of the boundary theory by the relevant operator with scaling dimension $Δ=\frac{d+2}{2}$ generates a logarithmic universal term to the entanglement entropy. As the smooth case, when the boundary CFT deformed by a relevant operator, we find that the entanglement entropy of singular surface also contains a new logarithmic term which is due to relevant perturbation of the conformal field theory, and depends on the scaling dimension of relevant operator. We also find for extended singular surfaces, $c_{n}\times R^{m}$, as well as logarithmic term, the new universal double logarithmic terms may appear depending on the scaling dimension of relevant operator and spacetime dimensions. These new terms are due to relevant perturbation of the boundary theory.

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arXiv2018

Entanglement entropy of singular surfaces under relevant deformations in holography

In the vacuum state of a CFT, the entanglement entropy of singular surfaces contains a logarithmic universal term which is only due to the singularity of the entangling surface. We consider the relevant perturbation of a three dimensional CFT for singular entangling surface. We observe that in addition to the universal term due to the entangling surface, there is a new logarithmic term which corresponds to a relevant perturbation of the conformal field theory with a coefficient depending on the scaling dimension of the relevant operator. We also find a new power law divergence in the holographic entanglement entropy. In addition, we study the effect of a relevant perturbation in the Gauss-Bonnet gravity for a singular entangling surface. Again a logarithmic term shows up. This new term is proportional to both the dimension of the relevant operator and the Gauss-Bonnet coupling. We also introduce the renormalized entanglement entropy for a kink region which in the UV limit reduces to a universal positive finite term.

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