arXiv subjects

Madison Hammond

Publications and source records attributed to Madison Hammond.

6 recordsLinked to original sources

arXiv2026

Holographic Spread Complexity at Fixed Charge: Routhians, Branes and Strings

Holographic spread (Krylov) complexity relates the growth of a boundary state's complexity to the proper radial momentum of a probe falling into the bulk. Unitary evolution makes spread complexity an even function of time. We show that this requirement fails whenever a probe carries a conserved Noether charge and is described by its unreduced Lagrangian. The cure is simple and universal: passing to the Routhian of the fixed-charge sector restores the correct short-time behaviour of the complexity. We establish this prescription from first principles and test it across an extensive family of probes: charged particles, non-BPS D-branes with detuned tension and charge, branes excited along internal isometries, worldvolume gauge fields, a fluctuating D0-brane in AdS$_4\times \mathbb{CP}^3$ and fundamental strings combining winding with rotation in AdS$_5\times \mathrm{S}^5$ complemented by further examples in AdS$_3\times \mathrm{S}^3\times T^4$, ABJM, and the charged Anabal\'on-Ross background. We then translate these results into Krylov-chain data, extracting Lanczos coefficients and Krylov-number correlators, and propose that complexity for charged, extended probes organises naturally into collective, fluctuation, charge and mixed contributions. This decomposition opens a concrete path toward a genuinely field-theoretic, multi-seed construction of holographic complexity.

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arXiv2026

Holographic Spread Complexity from Branes and Strings

We study Krylov spread complexity in holographic theories using genuine string-theory probes. Building on the proposal that the growth rate of spread complexity is measured by a proper momentum in the bulk, we embed the falling-particle picture in top-down examples. We first analyse a D0 brane in the type IIA AdS$_4\times {\mathbb{CP}}^3$ background dual to ABJM theory, identifying it with a dressed monopole operator in the boundary CFT. For purely radial motion the proper-momentum prescription reproduces the expected quadratic growth of the complexity. When the probe carries momentum along an isometric direction, the naive prescription gives an apparent conflict with the short-time behaviour required of Krylov complexity. We propose that the correct fixed-charge description is obtained by Legendre transforming to the Routhian. We support the D0-brane interpretation through the regulated monopole two-point function, whose survival amplitude determines the Krylov moments, and we show that radial fluctuations give controlled corrections to the effective energy governing the complexity growth. We then extend the analysis to a rotating non-BPS D3 brane in AdS$_5\times S^5$, where angular momentum produces a centrifugal barrier and a sharp condition for radial in-fall. In the falling regime the Routhian prescription again gives the correct short-time behaviour. Finally, we consider a wound fundamental string in AdS$_5\times S^5$, which reduces to an effective massive falling particle. This clarifies the distinction between Noether charges, which require a fixed-charge Routhian treatment, and winding data, which enter through the effective mass. Our results provide a string-theoretic realisation of holographic spread complexity for point-like and extended excitations, making manifest their dependence on field theory parameters.

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arXiv2026

Holographic observables in TsT deformations of confining theories

We construct new families of type-IIB supergravity solutions by employing TsT transformations on the ten-dimensional geometry that arises after the uplift of the five-dimensional soliton solution of Anabal\'on, Nastase, and Oyarzo. In particular, we identify two marginal and two dipole deformations of the uplifted geometry. We then analyse a plethora of holographic observables -- including Wilson loops, `t~Hooft loops, Page charges, entanglement entropy, and central charge -- and compare their behaviour across the different deformed backgrounds.

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arXiv2025

Supersymmetric AdS Solitons, Coulomb Branch Flows and Twisted Compactifications

This work, which accompanies [1], is about constructing smooth solutions in type II and eleven dimensional supergravity which describe supersymmetry preserving RG flows from four-dimensional SCFTs in the UV to three-dimensional SQFTs in the IR, through holography. We show that all the different UV fixed points flow to theories which confine external quarks and have a mass gap. We proceed by presenting extended calculations of a plethora of observables and analyse the dual field theories in great detail. This includes a boundary analysis and application of holographic renormalization methods in the simplest case of the type IIB solution. Many of the observables computed here have a universal behaviour: they factorize into two parts, one of which includes information about the UV SCFTs, and the other describing the dynamics of the RG flow, which is the same regardless of the UV fixed point.

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arXiv2025

Holographic Entanglement Entropy in Quiver Theories

This work presents a study of the entanglement entropy (EE) in a class of four-dimensional ${\cal N}=1$ linear quiver SCFTs deformed by the presence of a VEV. We review the holographic backgrounds dual to these theories, and calculate the EE for different Ryu-Takayanagi embeddings. We allow the embeddings to explore, in addition to the usual spatial direction, the internal coordinate $z$, associated with the quiver degrees of freedom. Via the numerical optimization of splines on triangulations, we find the minimal configuration and the value of the EE for the different embeddings and quiver parameters. Our results agree with previous studies showcasing phase transitions in the EE. We also provide novel results illuminating the dependence of the EE on the fundamental and gauge degrees of freedom, signaling partial deconfinement, which are worthy of further study.

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arXiv2025

Universal Observables, SUSY RG-Flows and Holography

We construct and analyse infinite classes of regular supergravity backgrounds dual to four-dimensional superconformal field theories (SCFTs) compactified on a circle with a supersymmetry-preserving twist. These flows lead to three-dimensional gapped QFTs preserving four supercharges. The solutions arise in Type IIB, Type IIA, and eleven-dimensional supergravity, and generalise known constructions by incorporating deformations that avoid typical singularities associated with the holographic description of the Coulomb branch of the CFT. We examine several observables: Wilson loops, holographic central charges, and complexity. We show they exhibit a universal factorisation, with each observable decomposing into a UV-CFT contribution times a flow-dependent factor. We also explore the parameter regimes where higher-curvature corrections become relevant, affecting the physical interpretation of certain observables. Our findings provide new insights into universal features of holographic RG flows and resolve a puzzle related to complexity in these systems.

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