arXiv subjects

Ronnie Rodgers

Publications and source records attributed to Ronnie Rodgers.

At least 19 recordsLinked to original sources

arXiv2026

Holomorphic D-brane embeddings in D-brane backgrounds

We describe families of probe D$q$-brane embeddings in the extremal black D$p$-brane backgrounds of type IIA and type IIB supergravity, specified by an arbitrary holomorphic function of a complex coordinate on the worldvolume of the D$q$-branes. These embeddings preserve one-quarter of the supersymmetry of the D$p$-brane background, or sometimes one-half of the supersymmetry when $p = q$. We discuss the holography of two example families of holomorphic probe branes in the near-horizon limit of the D3-brane background. The first is probe D5-branes, dual to defect hypermultiplets with a holomorphic mass, which in the infrared flow to Wilson lines located at the zeros of the mass. The second is probe D3-branes, holographically dual to states in the presence of Gukov--Witten surface defects in the dual $\mathcal{N}=4$ supersymmetric Yang--Mills theory.

hep-th↗

arXiv2025

Supersymmetric Holomorphic Masses in AdS/CFT with Flavour

In type IIB supergravity (SUGRA), in the extremal background of a number N_c of D3-branes we consider a number N_f of probe D7-branes extended along all four D3-brane directions, (x_0,x_1,x_2,x_3). Using (x_2,x_3) to define complex coordinates (z,\bar{z}) and defining the D7-branes' worldvolume scalars as (y,\bar{y}), we prove that any holomorphic function y(z) or antiholomorphic function y(\bar{z}) is a BPS solution of the D7-branes' equations of motion preserving N=(4,0) or (0,4) supersymmetry (SUSY) along (x_0,x_1), respectively. In the near-horizon geometry, five-dimensional Anti-de Sitter (AdS) spacetime times a five-sphere, the AdS/Conformal Field Theory correspondence states that type IIB SUGRA is holographically dual to four-dimensional N=4 supersymmetric SU(N_c) Yang-Mills theory at large N_c and large 't Hooft coupling, and the N_f D7-branes are dual to N_f N=2 hypermultiplets in the fundamental representation, i.e. flavour fields. Our D7-brane solutions are dual to a position-dependent hypermultiplet mass m that is holomorphic, m(z), or antiholomorphic, m(\bar{z}). We provide field theory proofs, valid for any N_c, N_f, and 't Hooft coupling, that such m preserve N=(4,0) or (0,4) SUSY along (x_0,x_1). We also perform holographic calculations with probe D7-branes to show that the theory with such m has zero energy and zero expectation value of the mass operator, and that a zero of m is dual to a superconformal defect described by chiral fermions along (x_0,x_1).

hep-th↗

arXiv2025

Entanglement C-functions of defects and interfaces in $\mathcal{N}=4$ supersymmetric Yang-Mills theory

We consider planar codimension-one defects and interfaces in $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory, realized by the D3/D5-brane intersection. Working in the probe limit, where the number of D5-branes is small compared to the number of D3-branes, we obtain analytic results for the holographic entanglement entropy of a ball-shaped region centered on the defect. A defect renormalization group flow is triggered by giving the defect hypermultiplets a mass, which corresponds to separating the D3- and D5-branes. Along this flow the entanglement C-function decreases monotonically. We also allow the D5-branes to carry worldvolume flux corresponding to dissolved D3-branes, in which case the setup describes an interface between two copies of $\mathcal{N}=4$ SYM theory with different gauge groups, where an RG flow is triggered by placing one side of the interface onto the Coulomb branch. Here we again find monotonic behavior of the entanglement C-function, although its interpretation as a measure of effective degrees of freedom is problematic. We investigate possible alternative measures of degrees of freedom.

hep-th↗

arXiv2025

Light dilaton near critical points in top-down holography

We study a class of UV-complete, strongly coupled, confining three-dimensional field theories, that exhibit a novel stabilisation mechanism for the mass of the lightest scalar composite state, relying on the existence of a critical point. The theories admit a holographic dual description in terms of regular backgrounds in eleven-dimensional supergravity. Their phase diagram includes a line of first-order phase transitions ending at the critical point, where the transition becomes of second order. We calculate the mass spectrum of bound states of the field theory, by considering fluctuations around the background solutions, and find that, near the critical point, a hierarchy of scales develops, such that one state becomes parametrically light. We identify this state as the dilaton, the pseudo-Nambu-Goldstone boson associated with the spontaneous breaking of approximate scale invariance. This stabilisation mechanism might be exploited to address hierarchy problems in particle and astroparticle physics.

hep-th↗

arXiv2024

Conductivities and excitations of a holographic flavour brane Weyl semimetal

We compute the electrical conductivities at non-zero frequency in a top-down holographic model of a Weyl semimetal, consisting of $\mathcal{N}=4$ supersymmetric $\mathrm{SU}(N_c)$ Yang--Mills theory coupled to $\mathcal{N}=2$ hypermultiplets with mass $m$, subject to an applied axial vector field $b$. The model exhibits a first-order phase transition between a Weyl semimetal phase at small $m/b$ and an insulating phase at large $m/b$. The conductivities develop peaks and troughs as functions of real frequency at low temperatures and for $m/b$ close to the phase transition. We compute the poles of the conductivities as functions of complex frequency, finding poles with small imaginary part at low temperatures and close to the phase transition.

hep-th↗

arXiv2024

Entanglement R\'{e}nyi entropies in celestial holography

Celestial holography is the conjecture that scattering amplitudes in $(d+2)$-dimensional asymptotically Minkowski spacetimes are dual to correlators of a $d$-dimensional conformal field theory (CFT) on the celestial sphere, called the celestial CFT (CCFT). In a CFT, we can calculate sub-region entanglement R\'{e}nyi entropies (EREs), including entanglement entropy (EE), from correlators of twist operators, via the replica trick. We argue that CCFT twist operators are holographically dual to cosmic branes in the $(d+2)$-dimensional spacetime, and that their correlators are holographically dual to the $(d+2)$-dimensional partition function (the vacuum-to-vacuum scattering amplitude) in the presence of these cosmic branes. We hence compute the EREs of a spherical sub-region of the CCFT's conformal vacuum, finding the form dictated by conformal symmetry, including a universal contribution determined by the CCFT's sphere partition function (odd $d$) or Weyl anomaly (even $d$). We find that this universal contribution vanishes when $d=4$ mod $4$, and otherwise is proportional to $i$ times the $d^{\textrm{th}}$ power of the $(d+2)$-dimensional long-distance cutoff in Planck units.

hep-th↗

arXiv2024

Light holographic dilatons near critical points

We investigate the relation between the emergence of a dilaton in gapped (confining) field theories, and the presence of either complex fixed points or instabilities in the strongly coupled dynamics in two classes of bottom-up holographic models. We demonstrate that in one of the two classes there is a critical line of first-order phase transitions (at zero temperature) that terminates at a critical point. We calculate the mass spectrum of fluctuations of the associated regular gravity backgrounds, which we interpret as bound states in the dual field theories. In proximity to the second-order phase transition, we find a parametrically light scalar state, and its composition leads us to identify it as a dilaton.

hep-th↗

arXiv2022

Nodal-antinodal dichotomy from anisotropic quantum critical continua in holographic models

We demonstrate that the absence of stable quasiparticle excitations on parts of the Fermi surface, similar to the "nodal-antinodal dichotomy" in underdoped cuprate superconductors, can be reproduced in models of strongly correlated electrons defined via a holographic dual. We show analytically that the anisotropy of the quantum critical continuum, which is a feature of these models, may lead to washing out the quasiparticle peak in one direction while leaving it intact in the perpendicular one. The effect relies on the qualitatively different scaling of the self-energy in different directions. Using the explicit example of the anisotropic Q-lattice model, we demonstrate how this effect emerges due to specific features of the near horizon geometry of the black hole in the dual description.

cond-mat.str-el↗

arXiv2022

Boost-invariant superfluid flows

We present some exact solutions to the ideal hydrodynamics of a relativistic superfluid with an almost-conformal equation of state. The solutions have stress tensors which are invariant under Lorentz boosts in one direction, and represent superfluid generalisations of the Bjorken and Gubser flows. We also study corrections to the flows in first-order hydrodynamics, arguing that dissipation is dominated by the shear viscosity. We present some simple numerical solutions for these viscous corrections. Finally, we estimate the size of corrections to the flows arising when the spontaneously broken $\mathrm{U}(1)$ symmetry responsible for superfluidity is only approximate, giving the corresponding Goldstone boson a small non-zero mass. We find that the massless solutions can still provide good approximations at sufficiently small spatial rapidities.

hep-th↗

arXiv2021

Thermodynamics and transport of holographic nodal line semimetals

We study various thermodynamic and transport properties of a holographic model of a nodal line semimetal (NLSM) at finite temperature, including the quantum phase transition to a topologically trivial phase, with Dirac semimetal-like conductivity. At zero temperature, composite fermion spectral functions obtained from holography are known to exhibit multiple Fermi surfaces. Similarly, for the holographic NLSM we observe multiple nodal lines instead of just one. We show, however, that as the temperature is raised these nodal lines broaden and disappear into the continuum one by one, so there is a finite range of temperatures for which there is only a single nodal line visible in the spectrum. We compute several transport coefficients in the holographic NLSM as a function of temperature, namely the charge and thermal conductivities, and the shear viscosities. By adding a new non-linear coupling to the model we are able to control the low frequency limit of the electrical conductivity in the direction orthogonal to the plane of the nodal line, allowing us to better match the conductivity of real NLSMs. The boundary quantum field theory is anisotropic and therefore has explicitly broken Lorentz invariance, which leads to a stress tensor that is not symmetric. This has important consequences for the energy and momentum transport: the thermal conductivity at vanishing charge density is not simply fixed by a Ward identity, and there are a much larger number of independent shear viscosities than in a Lorentz-invariant system.

hep-th↗

arXiv2020

A Weyl Semimetal from AdS/CFT with Flavour

We construct a top-down holographic model of Weyl semimetal states using $(3+1)$-dimensional $\mathcal{N}=4$ supersymmetric $SU(N_c)$ Yang-Mills theory, at large $N_c$ and strong coupling, coupled to a number $N_f \ll N_c$ of $\mathcal{N}=2$ hypermultiplets with mass $m$. A $U(1)$ subgroup of the R-symmetry acts on the hypermultiplet fermions as an axial symmetry. In the presence of a constant external axial gauge field in a spatial direction, $b$, we find the defining characteristic of a Weyl semi-metal: a quantum phase transition as $m/b$ increases, from a topological state with non-zero anomalous Hall conductivity to a trivial insulator. The transition is first order. Remarkably, the anomalous Hall conductivity is independent of the hypermultiplet mass, taking the value dictated by the axial anomaly. At non-zero temperature the transition remains first order, and the anomalous Hall conductivity acquires non-trivial dependence on the hypermultiplet mass and temperature.

hep-th↗

arXiv2020

Holographic Entanglement Entropy of the Coulomb Branch

We compute entanglement entropy (EE) of a spherical region in $(3+1)$-dimensional $\mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory in states described holographically by probe D3-branes in $AdS_5 \times S^5$. We do so by generalising methods for computing EE from a probe brane action without having to determine the probe's back-reaction. On the Coulomb branch with $SU(N)$ broken to $SU(N-1)\times U(1)$, we find the EE monotonically decreases as the sphere's radius increases, consistent with the $a$-theorem. The EE of a symmetric-representation Wilson line screened in $SU(N-1)$ also monotonically decreases, although no known physical principle requires this. A spherical soliton separating $SU(N)$ inside from $SU(N-1)\times U(1)$ outside had been proposed to model an extremal black hole. However, we find the EE of a sphere at the soliton's radius does not scale with the surface area. For both the screened Wilson line and soliton, the EE at large radius is described by a position-dependent W-boson mass as a short-distance cutoff. Our holographic results for EE and one-point functions of the Lagrangian and stress-energy tensor show that at large distance the soliton looks like a Wilson line in a direct product of fundamental representations.

hep-th↗

arXiv2020

Holographic Coulomb Branch Solitons, Quasinormal Modes, and Black Holes

Four-dimensional $\mathcal{N}=4$ supersymmetric Yang-Mills theory, at a point on the Coulomb branch where $SU(N)$ gauge symmetry is spontaneously broken to $SU(N-1)\times U(1)$, admits BPS solitons describing a spherical shell of electric and/or magnetic charges enclosing a region of unbroken gauge symmetry. These solitons have been proposed as gauge theory models for certain features of asymptotically flat extremal black holes. In the 't Hooft large $N$ limit with large 't Hooft coupling, these solitons are holographically dual to certain probe D3-branes in the $AdS_5 \times S^5$ solution of type IIB supergravity. By studying linearised perturbations of these D3-branes, we show that the solitons support quasinormal modes with a spectrum of frequencies sharing both qualitative and quantitative features with asymptotically flat extremal black holes.

hep-th↗

arXiv2019

Entanglement and Excitations in Gauge/Gravity Duality

In this thesis, we study a variety of phenomena in strongly coupled quantum field theories by performing calculations in their gravitational duals. We compute entanglement entropy in a variety of holographic systems, paying particular attention to its long-distance behaviour, characterised by a term proportional to surface area. This term is known to decrease along Lorentz-invariant renormalisation group flows, suggesting that it may count massless degrees of freedom. We find that more general deformations may increase this area term, possibly indicating an enhanced number of long-distance degrees of freedom. We observe a correlation between this enhancement and the emergence of new scaling symmetry at long distances. Next, we study the spectrum of collective excitations in a holographic model of a non-Fermi liquid. At high temperatures, the spectrum of collective excitations includes hydrodynamic sound waves. As in similar models, we observe that sound-like modes also exist at low temperatures. Such modes are known as holographic zero sound. We study the changing properties of holographic zero sound and the emergence of hydrodynamic behaviour at high temperatures as we vary the parameters of the model. We find that for certain values of the parameters, the temperature-dependence of holographic zero sound qualitatively resembles that of a normal Fermi liquid. Finally, we study the entanglement entropy contribution of surface defects in a six-dimensional quantum field theory of relevance to M-theory, which is a candidate theory of quantum gravity. We find that the entanglement entropy does not montonically decrease along renormalisation group flows on these defects, ruling it out as a potential measure of degrees of freedom. On the other hand, we find that two of the contributions of the defect to the Weyl anomaly of the quantum field theory decrease along all of the flows that we study.

hep-th↗

arXiv2019

Holographic Wilson Lines as Screened Impurities

In Landau Fermi liquids, screened impurities support quasi-bound states, representing electrons bound to the impurity but making virtual excursions away. Signals of these quasi-bound states are electron-impurity scattering phase shifts and the corresponding resonances in cross sections. We consider large-$N$, strongly-coupled $(3+1)$-dimensional $\mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory on the Coulomb branch, where an adjoint scalar has a non-zero expectation value that breaks $SU(N) \to SU(N-1) \times U(1)$. In the holographic dual we re-visit well-known solutions for a probe D3-brane that describe this theory with a symmetric-representation Wilson line "impurity." We present evidence that the adjoint scalar screens the Wilson line, by showing that quasi-bound states form at the impurity, producing $U(1)$-impurity scattering phase shifts and corresponding resonances in cross sections. The quasi-bound states appear holographically as quasi-normal modes of probe D3-brane fields, even in the absence of a black hole horizon, via a mechanism that we argue is generic to screened defects in holography. We also argue that well-known generalisations of these probe D3-brane solutions can describe lattices of screened Wilson/'t Hooft line impurities.

hep-th↗

arXiv2018

From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects

We study whether the relations between the Weyl anomaly, entanglement entropy (EE), and thermal entropy of a two-dimensional (2D) conformal field theory (CFT) extend to 2D boundaries of 3D CFTs, or 2D defects of $D \geq 3$ CFTs. The Weyl anomaly of a 2D boundary or defect defines two or three central charges, respectively. One of these, $b$, obeys a c-theorem, as in 2D CFT. For a 2D defect, we show that another, $d_2$, interpreted as the defect's `conformal dimension,' must be non-negative by the Averaged Null Energy Condition (ANEC). We show that the EE of a sphere centered on a planar defect has a logarithmic contribution from the defect fixed by $b$ and $d_2$. Using this and known holographic results, we compute $b$ and $d_2$ for 1/2-BPS surface operators in the maximally supersymmetric (SUSY) 4D and 6D CFTs. The results are consistent with $b$'s c-theorem. Via free field and holographic examples we show that no universal `Cardy formula' relates the central charges to thermal entropy.

hep-th↗

arXiv2018

Wilson Surface Central Charge from Holographic Entanglement Entropy

We use entanglement entropy to define a central charge associated to a two-dimensional defect or boundary in a conformal field theory (CFT). We present holographic calculations of this central charge for several maximally supersymmetric CFTs dual to eleven-dimensional supergravity in Anti-de Sitter space, namely the M5-brane theory with a Wilson surface defect and three-dimensional CFTs related to the M2-brane theory with a boundary. Our results for the central charge depend on a partition of the number of M2-branes, $N$, ending on the number of M5-branes, $M$. For the Wilson surface, the partition specifies a representation of the gauge algebra, and we write our result for the central charge in a compact form in terms of the algebra's Weyl vector and the representation's highest weight vector. We explore how the central charge scales with $N$ and $M$ for some examples of partitions. In general the central charge does not scale as $M^3$ or $N^{3/2}$, the number of degrees of freedom of the M5- or M2-brane theory at large $M$ or $N$, respectively.

hep-th↗

arXiv2018

Holographic entanglement entropy from probe M-theory branes

We compute the holographic entanglement entropy contribution from planar two-dimensional defects in six-dimensional $\mathcal{N}=(2,0)$ superconformal field theory, holographically dual to probe M2- and M5-branes in $AdS_7 \times S^4$. In particular, we test the viability of the universal contribution of the defect to entanglement entropy as a candidate $C$-function. We find that this coefficient is not monotonic under defect renormalization group flows triggered by the vacuum expectation value of a marginal operator. Another candidate $C$-function, the on-shell action inside the entanglement wedge, monotonically decreases under the flows we study.

hep-th↗