arXiv subjects

Amr Ahmadain

Publications and source records attributed to Amr Ahmadain.

13 recordsLinked to original sources

arXiv2026

A Worldsheet Derivation of the Classical Off-shell Boundary Action for the Dilaton in Half-Space

We use the method of images to present a worldsheet derivation of the sphere partition function for the dilaton in half-space to leading order in $α'$ with Neumann boundary conditions. We use Tseytlin's sphere prescription to obtain the total (bulk and boundary) off-shell classical bosonic string action for the dilaton in half-space and show that it satisfies the requirement for a well-defined variational principle

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arXiv2026

The GHY boundary term from the string worldsheet to linear order

Using the method of images we derive the boundary term of the Einstein-$Γ^2$ action in half-space from the spherical worldsheet to first order in $α'$ and to linear order in the metric perturbation around flat half-space. The $Γ^2$ action, written down by Einstein more than 100 years ago, includes a boundary term that consists of the Gibbons-Hawking-York action along with two additional terms that are functions of the metric, normal vector, and tangential derivatives. With this boundary term, the total (bulk + boundary) sphere effective action has a well-posed variational principle for Dirichlet boundary conditions.

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arXiv2026

Closed String Field Theory in 25.99 Dimensions

We return to and refine Zwiebach's formulation of closed string field theory (CSFT) built around non-critical backgrounds [1,2], restricting our attention to genus zero. The structure involves a special string state $F$ that encodes the failure of worldsheet BRST invariance, and a metric-dependent descent operator $\mathcal{B}$ adapted to the Weyl frame. We construct the mixed moduli spaces needed for the classical BV action, prove their existence, and extend the Sen-Zwiebach background independence argument to first order off of the conformal locus. We apply the formalism to the mildest deviation away from criticality - worldsheet CFTs with nonzero central charge: we consider both D=26-$ε$ dimensional flat space and linear dilaton profiles in bosonic string theory, focusing for simplicity on building solutions that depend on only one of the D dimensions.

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arXiv2025

Strings at the Tip of the Cone and Black Hole Entropy From the Worldsheet: Part I

We study the nonlinear sigma model (NLSM) worldsheet action describing the motion of closed bosonic strings in the target space of a two-dimensional (2D) flat cone in polar coordinates. We calculate the cylinder partition function. We first place the cylindrical worldsheet on a rectangular lattice before taking the continuum limit. We find an integer number of string configurations on the worldsheet, which we call line defects, that run from one boundary of the cylinder to the other. We insert two sources (conical defects) at each boundary and fix the two ends of the line defect by Dirichlet boundary conditions to a point $r_c$ in target space. In target space, a line defect appears as an Susskind\&Uglum-type open string ending on $r_c$. We compute the semiclassical contribution to the off-shell cylinder amplitude by saddle point approximation. The amplitude has an interesting infrared (IR) divergence structure that depends on the given range of the cone angle. We then compute the entropy by varying the cone angle. In a particular renormalization scheme that relates the ultraviolet (UV) and to the infrared (IR) limits of the modulus integral, we find the entropy to be free of IR divergences but linearly dependent on the radial cutoff. We argue that our calculation provides a well-defined state on a constant Euclidean-time slice directly from the string worldsheet. We also study the 2D flat cone NLSM without discretization. We compute the entropy from the off-shell stationary action and show it is finite in each winding sector $W$ with a maximum at $r_c=\sqrt{α'}/|W|$. After summing over all winding sectors, it still has a finite maximum in the UV limit but for $r_c >0$.

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arXiv2025

A Background-Independent Closed String Action at Tree Level

We propose an off-shell bosonic string action that removes the renormalization window constraint of [1]. To all orders in conformal perturbation theory, this action allows for deformations of the worldsheet theory by any primary or descendant irrelevant deformation. Non-perturbatively, this action has no spurious solutions on the space of all worldsheet theories with a unitary matter sector that flows from a UV fixed point. We find that non-minimal couplings dressed with more than one factor of the Ricci curvature behave as gauge redundancies. As part of our investigation of this action, we find non-smooth behavior in the Zamolodchikov $C$-function. Our results mostly apply to Euclidean-signature target spaces, but can be extended to Lorentzian backgrounds which are invariant under time translations and CTO symmetry.

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arXiv2024

Off-Shell Strings I: S-matrix and Action

We explain why Tseytlin's off-shell formulation of string theory is well-defined. Although quantizing strings on an off-shell background requires an arbitrary choice of Weyl frame, this choice is not physically significant since it can be absorbed into a field redefinition of the target space fields. The off-shell formalism is particularly subtle at tree-level, due to the treatment of the noncompact conformal Killing group SL(2,$\mathbb{C}$) of the sphere. We prove that Tseytlin's sphere prescriptions recover the standard tree-level Lorentzian S-matrix, and show how to extract the stringy $i\varepsilon$ prescription from the UV cutoff on the worldsheet. We also demonstrate that the correct tree-level equations of motion are obtained to all orders in perturbation theory in $g_s$ and $α^{\prime}$, and illuminate the close connection between the string action and the c-theorem.

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arXiv2024

Off-Shell Strings II: Black Hole Entropy

In 1994, Susskind and Uglum argued that it is possible to derive the Bekenstein-Hawking entropy $A/4G_N$ from string theory. In this article we explain the conceptual underpinnings of this argument, while elucidating its relationship to induced gravity and ER=EPR. Following an off-shell calculation by Tseytlin, we explicitly derive the classical closed string effective action from sphere diagrams at leading order in $α^{\prime}$. We then show how to use this to obtain black hole entropy from the RG flow of the NLSM on conical manifolds. (We also briefly discuss the more problematic ``open string picture'' of Susskind and Uglum, in which strings end on the horizon.) We then compare these off-shell results with the rival ``orbifold replica trick'' using the on-shell $\mathbb{C}/Z_{N}$ background, which does not account for the leading order Bekenstein-Hawking entropy -- unless perhaps tachyons are allowed to condense on the orbifold. Possible connections to the ER=EPR conjecture are explored. Finally, we discuss prospects for various extensions, including prospects for deriving holographic entanglement entropy in the bulk of AdS.

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arXiv2024

A Comment on Deriving the Gibbons-Hawking-York Term From the String Worldsheet

In this note, we show that the noncovariant metric boundary term obtained from the nonlinear sigma model worldsheet derivation of the bulk off-shell sphere partition function is closely related to the Einstein boundary term in the Gamma-Gamma noncovariant action. In fact, when expressed in terms of the trace of the extrinsic curvature tensor, we illustrate that this boundary term has one-half the coefficient of the Gibbons-Hawking-York boundary term required such that the total (bulk plus boundary) off-shell classical action has a well-posed variational principle with Dirichlet boundary conditions.

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arXiv2024

Boundary Description of Microstates of the Two-Dimensional Black Hole

We identify the microstates of the non supersymmetric, asymptotically flat 2d black hole in the dual c=1 matrix quantum mechanics (MQM). We calculate the partition function of the theory using Hamiltonian methods and reproduce one of two conflicting results found by Kazakov and Tseytlin. We find the entropy by counting states and the energy by solving the Schrodinger equation. The dominant contribution to the partition function in the double scaling limit is a novel bound state that can be considered an explicit dual of the black hole microstates. This bound state is long lived and evaporates slowly, exactly like a black hole in asymptotically flat space.

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arXiv2021

Emergent geometry and path integral optimization for a Lifshitz action

Extending the background metric optimization procedure for Euclidean path integrals of two-dimensional conformal field theories, introduced by Caputa et al. (Phys. Rev. Lett. 119, 071602 (2017)), to a $z=2$ anisotropically scale-invariant $(2+1)$-dimensional Lifshitz field theory of a free massless scalar field, we find optimal geometries for static and dynamic correlation functions. For the static correlation functions, the optimal background metric is equivalent to an AdS metric on a Poincare patch, while for dynamical correlation functions, we find Lifshitz like metric. This results suggest that a MERA-like tensor network, perhaps without unitarity, would still be considered an optimal background spacetime configuration for the numerical description of this system, even though the classical action we start with is not a conformal field theory.

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arXiv2019

A (1+1)-dimensional Lifshitz Weyl Anomaly From a Schr$\mathrm{\ddot{o}}$dinger-invariant Non-relativistic Chern-Simons Action

The main result of this paper is that the Weyl anomaly of a $z=2$ (1+1)-dimensional Lifshitz effective action can be derived from a (2+1)-dimensional non-relativistic Schr$\mathrm{\ddot{o}}$dinger-invariant Chern-Simons (NRSCS) action which was shown to be equivalent to a specific Weyl-invariant non-projectable Horava-Lifshitz action of gravity. On a manifold with a boundary, we will show that the (1+1)-dimensional Lifshitz Weyl anomaly can be derived from a specific term, the torsional CS (tCS) term, in the NRSCS action built from the gauge fields of the Weyl and special conformal symmetry generators of the centrally-extended Schr$\mathrm{\ddot{o}}$dinger algebra. We also focus on the $z=1$ Lifshitz Weyl anomaly and attempt to elicit its geometric and physical nature, in particular its relationship with the Lorentz anomaly of a (1+1)-dimensional CFT effective actions. We show that it is directly related to the curvature scalar of the dual Lorentz connection, the integral of which is known to be a topological invariant. We also point out that making the anomalous Lifshitz quantum effective action Weyl-invariant amounts to obtaining the equation of motion for a stationary chiral boson which happens to be the spatial-component of the acceleration vector. By putting boundary conditions on the spatial slices, the time dependence of the lapse function in the Arnowitt, Deser and Misner (ADM) decomposition is eliminated and the result is a Rindler metric. We finally discuss several issues related to the (1+1)-dimensional Lifshitz Weyl anomaly regarding edge physics of fractional quantum Hall states and anomaly cancellation by anomaly inflow.

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arXiv2018

Holographic rainbow networks for colorful Motzkin and Fredkin spin chains

We present bulk tensor networks that exactly represent the ground states of a continuous family of one-dimensional frustration-free Hamiltonians. These states, which are known as area-deformed Motzkin and Fredkin states, exhibit a novel quantum phase transition. By tuning a single parameter, they go from a phase obeying an area law to a highly entangled rainbow phase, where the half-chain entropy scales with the volume. Using the representation of these ground states as superpositions of random walks, we introduce tensor networks for these ground states where local and global rules of the walker are baked into bulk tensors, thereby providing an efficient description of the ground states (some of which satisfy a volume law scaling of entanglement entropy).

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arXiv2016

Quantum phase transition from bounded to extensive entanglement entropy in a frustration-free spin chain

We introduce a continuous family of frustration-free Hamiltonians with exactly solvable ground states. We prove that the {ground state of our model is non-degenerate and exhibits} a novel quantum phase transition from bounded entanglement entropy to a massively entangled state with volume entropy scaling. The ground state may be interpreted as a deformation away from the uniform superposition of colored Motzkin paths, showed by Movassagh and Shor to have a large (square-root) but sub-extensive scaling of entanglement into a state with an extensive entropy.

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