arXiv subjects

Carlos Nunez

Publications and source records attributed to Carlos Nunez.

At least 19 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

Complexity measures in holographic cascading theories with multiscale dynamics

Using the gravitational duals, we perform a systematic study of two notions of complexity in a family of three-dimensional gauge theories with rich infrared structure. For thermofield double states, we employ the complexity=volume prescription, which relates computational complexity to the volume of the dual Einstein-Rosen bridge. For one particle states created by the insertion of a local operator on the vacuum, we study their spreading in Krylov space, encoded holographically by the radial momentum of bulk excitations. We investigate these two notions of complexity across the parameter space of the theories, focusing on the two limiting values of a tunable parameter. Near the limit where the theories flow close to an intermediate conformal fixed point, both notions reveal distinct manifestations of ``walking'' dynamics. Near the opposite limit, computational complexity is largely insensitive to the confining nature of the ground state, whereas the frequency of oscillations in the Krylov spread complexity -- set by the emerging infrared scale -- is sensitive to the presence of confinement.

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arXiv2026

Krylov Complexity and $c$-function along RG Flows

We investigate Krylov spread complexity along holographic renormalisation-group flows using the proposal that its growth rate is captured by the proper radial momentum of an in-falling massive probe. We focus on the second time derivative of the complexity ${U}$, which is determined locally by the redshift and radial metric functions of the dual geometry. For Lorentz-invariant domain-wall flows preserving the spacetime dimension, we derive a new relation between ${U}$ and the covariant central charge $c_{\text{cov}}$. The decrease of the covariant central function towards the infrared is accompanied by a monotonic increase of the complexity acceleration. For the top-down Dp-brane family, we obtain a universal relation. We then examine flows across dimensions, including a twisted compactification from four to two dimensions and from six to four dimensions. In these examples $c_{\rm cov}$ and ${U }$ are co-monotonic, in sharp contrast with the inverse correlation characteristic of fixed-dimensional flows. We argue that this reversal reflects the reorganisation, rather than simple depletion, of degrees of freedom into lower-dimensional sectors under compactification. Our results identify complexity acceleration as a sensitive geometric diagnostic connecting information spreading, holographic central functions and RG evolution.

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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

Covariant unification of holographic c-functions

We propose a covariant holographic c-function, defined directly in a top-down background and constructed from the extrinsic curvature of codimension-two slices of the bulk geometry. The definition does not rely on a special choice of coordinates or on the existence of a consistent dimensional reduction. We show that it unifies previous foliation-based holographic c-functions into a single covariant formula, reducing to them in the appropriate limits. We evaluate the covariant expression in a range of top-down string backgrounds, including conformal models, confining geometries, flows across dimensions, and the Klebanov-Murugan geometry, in which the holographic radial direction mixes with internal coordinates and which is not the uplift of a lower-dimensional solution. In all cases, the c-function behaves as expected: it interpolates monotonically between AdS fixed points when they are present and decreases towards zero in gapped infrared regions, while in the Klebanov-Murugan case we recover the correct fixed-point values and find evidence for monotonicity. We highlight open conceptual issues, including: the lack of a universal covariant definition of the holographic radial direction in the presence of a nontrivial internal manifold; the derivation of the flow from a bulk action; and the relation to the entanglement c-function.

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arXiv2026

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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arXiv2026

Holographic Krylov Complexity for Charged, Composite and Extended Probes

We study the holographic spread/Krylov complexity of operators with non-trivial internal structure and of genuinely extended operators. We first consider a massive particle in AdS$_5\times S^5$ carrying conserved $R$-charge, and show how motion in the internal space modifies the complexity growth, yielding a natural holographic realisation of symmetry-resolved Krylov complexity. We then move to probes that are effectively pointlike from the field-theory viewpoint but possess an intrinsic structure in the bulk: baryon-vertex configurations and giant gravitons. Our results indicate that, for this broad class of structured but pointlike probes, the leading large-time behaviour retains the characteristic form expected for local operators in conformal theories, while the internal structure and induced charges produce informative subleading effects. We also study a genuinely extended probe, a fundamental string falling in AdS while stretched along a spatial direction, as a model for the spread complexity of a non-local operator. In this case, although the leading behaviour still exhibits the expected growth pattern, the subleading terms and intermediate regimes differ qualitatively from those of pointlike probes. This provides concrete evidence that extended operators carry a finer notion of spread complexity, sensitive to their spatial structure. Our results broaden the class of probes for which holographic Krylov complexity can be analysed explicitly, clarify which features are universal and which depend on the nature of the operator, and open a promising route toward a sharper field-theory understanding of complexity for charged, composite and extended excitations.

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arXiv2026

Moduli space of ${\cal N}=4$ Super Yang-Mills from AdS/CFT

We study ${\cal N}=4$ super Yang-Mills theory compactified on a circle at zero temperature, with VEVs for two scalar bilinears and three independent current sources. We show that type IIB supergravity provides a complete holographic description of this setup, admitting both supersymmetric and non-supersymmetric AdS soliton solutions, which are asymptotically AdS$_5$ and smooth in the IR. The current sources correspond in (2+1) dimensions to Q-ball charge densities for $U(1)^3\subset SO(6)_R$, and are geometrically realized as twists along three angular directions of the $S^5$. We demonstrate that the bulk dynamics encodes the full vacuum structure of the dual field theory and explicitly reconstruct the supersymmetric moduli space.

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arXiv2026

Complexity and Operator Growth in Holographic 6d SCFTs

We study Krylov (spread) complexity in strongly coupled six-dimensional ${\cal N}=(1,0)$ superconformal field theories with holographic duals in massive type IIA supergravity. Extending recent holographic proposals relating Krylov complexity growth to the proper momentum of an infalling particle, we analyse the dynamics of massive geodesic probes in these geometries. In our setup, the bulk particle is allowed to move along three directions: the radial AdS coordinate, the internal $S^2$ associated with the $SU(2)_R$ symmetry, and the coordinate parametrising the quiver. In the dual field theory these motions encode, respectively, operator growth, the presence of R-symmetry charges, and spreading across different nodes of the quiver. We analyse the geodesic motion both analytically and numerically for representative quiver configurations. The motion along the quiver direction is typically damped and localised at early times, while the late-time behaviour is dominated by the radial AdS motion. As a consequence, the generalised proper momentum grows linearly at late times, consistent with expectations for Krylov complexity in conformal theories. The inclusion of angular momentum ($SU(2)_R$ charge) introduces additional constraints on the allowed motion and modifies the early-time dynamics while leaving the asymptotic behaviour unchanged. These results provide a first exploration of Krylov complexity in higher-dimensional holographic conformal theories and reveal how operator growth can probe both internal symmetries and quiver structure in strongly coupled conformal field theories.

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arXiv2026

Krylov Complexity, Confinement and Universality

We perform a systematic holographic study of Krylov complexity for a wide class of confining quantum field theories. Using the geometric prescription that identifies the time derivative of the complexity with the proper momentum of a massive probe, we analyse radial geodesics in several top-down gravity duals exhibiting confinement and a mass gap. In all geometries with a smooth infrared end-of-space we uncover a robust and universal qualitative feature: Krylov complexity exhibits oscillatory behaviour. The oscillation frequency is controlled by the confinement scale, while the amplitude depends on both the ultraviolet cutoff and the infrared scale. Additional conserved charges modify these patterns without altering their qualitative structure. We further compare our results with the Krylov complexity of the longitudinally perturbed Ising model. The qualitative agreement suggests that oscillatory behaviour of Krylov complexity constitutes a universal signature of confinement and provides a sensitive probe of infrared reorganisation in strongly coupled quantum field theories.

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arXiv2025

Holographic Krylov Complexity for Conformal Quiver Gauge Theories

We investigate holographic Krylov complexity in fully top-down AdS$_3$ and AdS$_2$ supergravity backgrounds dual to two-dimensional linear-quiver SCFTs and one-dimensional conformal quantum mechanics. In these geometries, the warp factors, dilaton and other fields depend non-trivially on the 'quiver coordinate' (denoted by $η$ in this paper). This $η$-coordinate encodes the color and flavor data of the dual theories. As a consequence, a massive probe following a holographic geodesic necessarily moves simultaneously in the radial AdS direction and along the 'quiver direction'. This produces new contributions to the proper momentum and hence to the rate of Krylov complexity growth, which is absent in bottom-up AdS models. We show that the $η$-motion is generically damped, with a time-scale governed by the UV cutoff of the geodesic problem, and modifies the early-time evolution of complexity in a quiver-dependent way. At late times, the $η$-dynamics freezes and the growth becomes universal, matching pure Poincare AdS predictions. Studying Abelian and non-Abelian T-dual backgrounds of AdS$_3\times S^3\times T^4$, quivers with localized flavor groups, and quivers with smeared flavor groups, we quantify how quiver parameters shape the operator-spreading dynamics. Our results provide a systematic characterization of Krylov complexity in top-down AdS$_3$/AdS$_2$ duals and reveal a holographic mechanism through which complexity probes both ultraviolet quiver structure and emergent infrared universality.

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arXiv2025

Holographic Krylov complexity in confining gauge theories

We study holographic Krylov complexity in the Anabalon-Ross solitonic background, a top-down Type IIB solution describing a twisted-circle compactification of ${\cal N}=4$ SYM that flows to a confining, gapped three-dimensional theory. Following the proposal that the time derivative of Krylov complexity is dual to the proper radial momentum of a falling bulk particle, we analyze probe geodesics in this geometry. We obtain exact analytic solutions for the radial trajectory in terms of elliptic functions, confirming and extending UV and IR asymptotic expansions. The proper momentum and resulting complexity exhibit oscillatory behaviour, which we interpret as a holographic signature of the finite Hilbert-space truncation induced by the UV cutoff together with the IR end-of-space. Our results provide a controlled top-down test of the spread-momentum correspondence and highlight qualitative differences between conformal and confining holographic dynamics.

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arXiv2025

Holographic Timelike Entanglement Across Dimensions

We develop a holographic framework for computing timelike entanglement entropy (tEE) in quantum field theories, extending the Ryu-Takayanagi prescription into Lorentzian settings. Using three broad classes of supergravity backgrounds, we derive both exact and approximate tEE expressions for slab, spherical, and hyperbolic regions, and relate them to the central charges of the dual conformal field theories. The method is applied to infinite families of supersymmetric linear quivers in dimensions from d=2 to d=6, showing that Liu-Mezei and slab central charges scale universally like the holographic central charge. We then analyse gapped and confining models, including twisted compactifications and wrapped brane constructions, identifying how a mass gap modifies tEE and when approximate formulas remain accurate. In all cases, we uncover robust scaling with invariant separations and signature dependent phase behaviour, distinguishing spacelike from timelike embeddings. Our results unify the treatment of tEE in both conformal and nonconformal theories, clarifying its role as a probe of causal structure, universal data, and nonperturbative dynamics in holography.

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arXiv2025

On entanglement c-functions in confining gauge field theories

Entanglement entropy has proven to be a powerful tool for probing renormalization group (RG) flows in quantum field theories, with c-functions derived from it serving as candidate measures of the effective number of degrees of freedom. While the monotonicity of such c-functions is well established in many settings, notable exceptions occur in theories with a mass scale. In this work, we investigate entanglement c-functions in the context of holographic RG flows, with a particular focus on flows across dimensions induced by circle compactifications. We argue that in spacetime dimensions $d \geq 4$, standard constructions of c-functions, which rely on higher derivatives of the entanglement entropy of either a ball or a cylinder, generically lead to non-monotonic behavior. Working with known dual geometries, we argue that the non-monotonicity stems not from any pathology or curvature singularity, but from a transition in the holographic Ryu--Takayanagi surface. In compactifications from four to three dimensions, we propose a modified construction that restores monotonicity in the infrared, although a fully monotonic ultraviolet extension remains elusive. Furthermore, motivated by entanglement entropy inequalities, we conjecture a bound on the cylinder entanglement c-function, which holds in all our examples.

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arXiv2025

Interpolating between Space-like and Time-like Entanglement via Holography

We study entanglement entropy for slab like regions in quantum field theories, using their holographic duals. We focus on the transition between space like and time like separations. By considering boosted subsystems in conformal and confining holographic backgrounds, we identify two classes of extremal surfaces: real ones (Type I) and complex surfaces (Type II). These interpolate between the usual Ryu Takayanagi prescription and its time like generalisations. We derive explicit expressions for the entanglement entropy in both conformal and confining cases. We discuss their behaviour across phase transitions and null limits. The interpolation between Type I and Type II surfaces reveals an analytic continuation of the extremal surface across the light cone. Our analysis also finds the existence of a Ryu Takayanagi surface (Type I) even for time like separations in the confining field theory case.

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arXiv2025

Twisted-Circle Compactifications of SQCD-like Theories and Holography

We construct and analyse holographic duals to a class of four-dimensional N = 1 SU($N_c$) SQCD-like theories compactified on a circle with an R-symmetry twist. The setup originates from type IIB backgrounds previously proposed as duals to SQCD with $N_f$ fundamental flavours. The U(1) R-symmetry is anomaly-free only if $ N_f = 2N_c$. We implement a supersymmetric twisted-circle reduction, holographically realised through a smoothly shrinking $S^1$ fibered over the internal U(1)$_R$ direction. We obtain new regular type IIB supergravity backgrounds that are valid only if the condition $N_f = 2N_c$ is satisfied--mirroring the anomaly cancellation requirement in the field theory. We compute various field-theoretic observables--including the Chern-Simons level, Wilson loop and the holographic central charge--showing the emergence of a 3D ${\cal N} = 2$ gapped phase consistent with a Chern-Simons TQFT. This work highlights the interplay between anomalies, supersymmetry, and geometry in the holographic realisation of compactified gauge theories with fundamental matter.

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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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arXiv2025

Time-like Entanglement Entropy: a top-down approach

We investigate the concept of time-like entanglement entropy (tEE) within the framework of holography. We introduce a robust top-down prescription for computing tEE in higher-dimensional QFTs, both conformal and confining, eliminating the ambiguities typically associated with analytic continuation from Euclidean to Lorentzian signatures. We present accurate analytic approximations for tEE and time-like separations in slab geometries. We establish a clear stability criterion for bulk embeddings and demonstrate that tEE serves as a powerful tool for computing CFT central charges, extending and strengthening previous results. Finally, we apply our framework to holographic confining backgrounds, revealing distinctive behaviours like phase transitions.

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