arXiv subjects

David Vegh

Publications and source records attributed to David Vegh.

At least 19 recordsLinked to original sources

arXiv2026

Fortuity and fragility in supersymmetric SYK

In the $\mathcal N=2$ supersymmetric SYK model with $N$ fermions, every BPS state is fortuitous: at fixed charge, it exists only over a finite range of $N$. Allowing the charge to increase, we show that BPS classes may instead be uplifted along lattice walks inside the fortuity window, potentially to arbitrarily large $N$. However, there is no canonical uplift. We therefore introduce a decoder $D$ whose spectrum quantifies exact uplift and its metric cost. We call the failure or increasing cost of uplifting harmonic representatives metric fragility. Chen's single-matrix model and the protected tower of the two-flavor SYK model realize bare and genuinely dressed mechanisms of perfect uplift, respectively. In the generic one-flavor model, exact uplift eventually fails. The Lin-Maldacena-Rozenberg-Shan-type operator $D^\dagger D$ exhibits level statistics consistent with the Gaussian unitary ensemble. Its eigenvalues quantify the metric continuity of BPS states across system size, while their correlations probe chaos within the BPS sector. Metric fragility and BPS chaos are thus encoded in complementary observables of the same operator, distinguishing chaotic BPS sectors from exactly solvable towers.

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arXiv2026

Quantum mechanical bootstrap without inequalities: SYK bilinear spectrum

We study a quantum mechanical system whose spectrum coincides with that of bilinear operators of the Sachdev-Ye-Kitaev model. The standard positivity-based quantum mechanical bootstrap is degenerate with respect to the boundary data: it does not distinguish the boundary conditions that select the SYK spectrum, and hence is insufficient to determine the eigenvalues. Instead, by considering fractional powers of operators, we obtain constraint equations that determine the spectrum without imposing positivity. The resulting roots converge to exact eigenvalues as the truncation order increases. We call this the direct bootstrap.

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arXiv2025

Krylov Complexity of Supersymmetric SYK Models

We study the effect of supersymmetry breaking on Krylov complexity in the $\mathcal{N}=2$ SYK model under irrelevant and mass deformations of the Hamiltonian. The irrelevant deformation breaks $\mathcal{N}=2$ supersymmetry down to $\mathcal{N}=1$, while the mass deformation breaks supersymmetry completely. Using Krylov subspace methods, we analyze the Lanczos sequence, Krylov dimension, complexity, and entropy of the undeformed model and both deformations at finite system size. Both deformations enlarge the Krylov space and raise the saturation complexity as the BPS degeneracy is lifted. For the system sizes explored, the irrelevant deformation drives the saturation complexity to roughly half the Krylov dimension, while the mass deformation decreases it over an intermediate range of deformation strengths as the system drifts toward integrability. These distinct behaviors reveal how the mechanism of supersymmetry breaking leaves an imprint on quantum complexity.

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arXiv2025

A folded string dual for the Sachdev-Ye-Kitaev model

We propose a folded string moving in rigid AdS$_2$ with imaginary radius squared as a dual of the Sachdev-Ye-Kitaev (SYK) model at its conformal fixed point. In standard AdS$_2$, the string is represented by two massless particles connected by straight string segments. The particles move at the speed of light, abruptly reversing direction at turning points. We describe the system using the lightcone coordinates of these points, with the Poisson structure obtained from the Peierls bracket. In AdS$_2$ with imaginary radius squared, quantization of the string's mass-squared in momentum-fraction space yields a P\"oschl-Teller equation, reproducing the SYK operator spectrum.

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arXiv2024

Quantizing the folded string in AdS$_2$

In two-dimensional flat space, the oscillatory motion of a closed folded string--or alternatively, two massless particles connected by a string--can be quantized using the 't Hooft equation. This paper presents an alternative method for quantizing the folded string in anti-de Sitter space. By using variables inspired by integrability, setting $g \equiv {(R_\text{AdS})^2 \over 2\pi \alpha'}$ to a specific p-dependent $\mathcal{O}(1)$ value, and applying a particular boundary condition to the antisymmetrized wavefunction, we obtain a spectrum that precisely matches that of fermion bilinear operators in the disorder-averaged Sachdev-Ye-Kitaev model with p-fermion interactions.

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arXiv2024

Quantum mechanical bootstrap on the interval: obtaining the exact spectrum

We show that for a particular model, the quantum mechanical bootstrap is capable of finding exact results. We consider a solvable system with Hamiltonian $H=SZ(1-Z)S$, where $Z$ and $S$ satisfy canonical commutation relations. While this model may appear unusual, using an appropriate coordinate transformation, the Schr\"odinger equation can be cast into a standard form with a P\"oschl-Teller-type potential. Since the system is defined on an interval, it is well-known that $S$ is not self-adjoint. Nevertheless, the bootstrap method can still be implemented, producing an infinite set of positivity constraints. Using a certain operator ordering, the energy eigenvalues are only constrained into bands. With an alternative ordering, however, we find that a finite number of constraints is sufficient to fix the low-lying energy levels exactly.

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arXiv2023

The 't Hooft equation as a quantum spectral curve

In an attempt to establish a link between different quantization methods, I examine the massless 't Hooft equation, which governs meson bound state wavefunctions in 2d SU(N) gauge theory in the large-N limit. The integral equation can also be obtained by lightcone quantizing a folded string in flat space. The folded string is a limiting case of a more general setup: a four-segmented string moving in AdS$_3$. I compute its classical spectral curve by using celestial variables and planar bipartite graphs (on-shell diagrams/brane tilings). The adjugate of the Kasteleyn matrix vanishes at two special points, which ensures that the string segments form a closed loop in target space. The Hamiltonian takes on a Ruijsenaars-Schneider form and the phase space is a coadjoint SL(2) orbit whose middle region has been removed. In AdS, the 't Hooft equation acquires an extra term, which has previously been proposed as an effective confining potential in QCD. After an integral transform, the equation can be inverted in terms of a finite difference equation. I show that this difference equation can be interpreted as the quantized (non-analytic) spectral curve of the string. I calculate the spectrum numerically, which interpolates between $M^2=n(n+1)$ in the tensionless limit and 't Hooft's nearly linear Regge trajectory at infinite AdS radius.

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arXiv2022

Complex geodesics in de Sitter space

The two-point function of a free massive scalar field on a fixed background can be evaluated in the large mass limit by using a semiclassical geodesic approximation. In de Sitter space, however, this poses a puzzle. Certain spacelike separated points are not connected by real geodesics despite the corresponding two-point function in the Bunch-Davies state being non-vanishing. We resolve this puzzle by considering complex geodesics after analytically continuing to the sphere. We compute one-loop corrections to the correlator and discuss the implications of our results to de Sitter holography.

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arXiv2022

What lies beyond the horizon of a holographic p-wave superconductor

We study the planar anti-de Sitter black hole in the p-wave holographic superconductor model. We identify a critical coupling value which determines the type of phase transition. Beyond the horizon, at specific temperatures flat spacetime emerges. Numerical analysis close to these temperatures demonstrates the appearance of a large number of alternating Kasner epochs.

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arXiv2021

Segmented strings, brane tilings, and the Y-system

I show that the motion of a closed string consisting of $n$ segments in AdS$_3$ can be embedded into the mutation dynamics of the $Y^{n,0}$ brane tiling. The determinant of the Kasteleyn matrix computes the spectral curve. The dynamics is governed by a Y-system with additional constraints ensuring that the string closes in target space. The constraints can be deformed by coupling the worldsheet to a background two-form whose field strength is proportional to the volume form.

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arXiv2021

Kasner geometries inside holographic superconductors

The recent study of holographic superconductors has shown the emergence of a Kasner universe behind the event horizon. This paper serves to add to the discussion by introducing two modifications to the holographic superconductor model: an axion field term and an Einstein-Maxwell-scalar (EMS) coupling term. We first discuss the effect the modification parameters have on the condensate then explore the black hole interior dynamics. Features previously identified in the interior are found in the model presented, including the collapse of the Einstein-Rosen bridge, Josephson oscillations and Kasner inversions/transitions. However, we find that by increasing the EMS coupling parameter, the collapse does not occur near the axion-Reissner-Nordstr\"om horizon and the oscillations are no longer present; the geometry entering into a Kasner regime after a large-$r$ collapse instead.

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arXiv2021

The spectral curve of segmented strings

I show how to compute the spectral curve of piecewise linear Nambu-Goto strings in three-dimensional anti-de Sitter spacetime in terms of `celestial' embedding variables.

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arXiv2021

Celestial fields on the string and the Schwarzian action

This paper describes the motion of a classical Nambu-Goto string in three-dimensional anti-de Sitter spacetime in terms of two `celestial' fields on the worldsheet. The fields correspond to retarded and advanced boundary times at which null rays emanating from the string reach the boundary. The formalism allows for a simple derivation of the Schwarzian action for near-AdS2 embeddings.

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arXiv2021

On compressing sinh-Gordon solutions

This paper is concerned with a class of approximate non-linear transformations that compress solutions of the (generalized) sinh-Gordon equation into parametrically small regions in two-dimensional spacetime. Given the sinh-Gordon field near a time-slice, a long Nambu-Goto string can be constructed in three-dimensional anti-de Sitter space. The string is then approximated to arbitrary accuracy by a slightly smoothed piecewise linear string of N segments. The corresponding sinh-Gordon field has a comb-like structure and its size is controlled by the amount of smoothing applied to the segmented string. In a (singular) large-N limit, the transformation commutes with time evolution. As an example, a static cosh-Gordon solution is discussed in detail. The corresponding smooth and segmented string solutions are obtained and the compressed cosh-Gordon potential is investigated.

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arXiv2021

Relativistic membrane solutions in AdS$_4$

In this note we discuss various classical membrane solutions in AdS$_4$ spacetime: simple embeddings given by polynomials in ambient space, solutions with non-linear waves, and piecewise linear solutions.

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arXiv2021

Pole-skipping and Rarita-Schwinger fields

In this note we analyse the equations of motion of a minimally coupled Rarita-Schwinger field near the horizon of an anti-de Sitter-Schwarzschild geometry. We find that at special complex values of the frequency and momentum there exist two independent regular solutions that are ingoing at the horizon. These special points in Fourier space are associated with the `pole-skipping' phenomenon in thermal two-point functions of operators that are holographically dual to the bulk fields. We find that the leading pole-skipping point is located at a positive imaginary frequency with the distance from the origin being equal to half of the Lyapunov exponent for maximally chaotic theories.

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arXiv2020

Horizon constraints on holographic Green's functions

We explore a new class of general properties of thermal holographic Green's functions that can be deduced from the near-horizon behaviour of classical perturbations in asymptotically anti-de Sitter spacetimes. We show that at negative imaginary Matsubara frequencies and appropriate complex values of the wavenumber the retarded Green's functions of generic operators are not uniquely defined, due to the lack of a unique ingoing solution for the bulk perturbations. From a boundary perspective these `pole-skipping' points correspond to locations in the complex frequency and momentum planes at which a line of poles of the retarded Green's function intersects with a line of zeroes. As a consequence the dispersion relations of collective modes in the boundary theory at energy scales $ω\sim T$ are directly constrained by the bulk dynamics near the black-brane horizon. For the case of conserved $U(1)$ current and energy-momentum tensor operators we give examples where the dispersion relations of hydrodynamic modes pass through a succession of pole-skipping points as real wavenumber is increased. We discuss implications of our results for transport, hydrodynamics and quantum chaos in holographic systems.

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arXiv2019

Fermionic pole-skipping in holography

We examine thermal Green's functions of fermionic operators in quantum field theories with gravity duals. The calculations are performed on the gravity side using ingoing Eddington-Finkelstein coordinates. We find that at negative imaginary Matsubara frequencies and special values of the wavenumber, there are multiple solutions to the bulk equations of motion that are ingoing at the horizon and thus the boundary Green's function is not uniquely defined. At these points in Fourier space a line of poles and a line of zeros of the correlator intersect. We analyze these `pole-skipping' points in three-dimensional asymptotically anti-de Sitter spacetimes where exact Green's functions are known. We then generalize the procedure to higher-dimensional spacetimes. We also discuss the special case of a fermion with half-integer mass in the BTZ background. We discuss the implications and possible generalizations of the results.

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