arXiv subjects

Alejandro Cabo-Bizet

Publications and source records attributed to Alejandro Cabo-Bizet.

At least 19 recordsLinked to original sources

arXiv2026

Projecting Gravitational Fluctuations onto Near-Horizon Throats

We show that, for stationary geometries whose linearized fluctuation equations separate into radial and angular Heun equations, a pair of diffeomorphisms projects the full problem onto two coupled, isospectral Gauss hypergeometric problems in complementary spacetime regions. This projection requires Robin boundary conditions to be imposed at the intersection between the complementary regions, which are uniquely fixed by requiring the two diffeomorphisms to match there. The method provides an independent derivation of recent results obtained from the correspondence between Heun connection coefficients and instanton partition functions in the Nekrasov-Shatashvili limit. As an application, we identify a subset of modes in Kerr-de Sitter and Kerr-anti-de Sitter black holes that, in the near-extremal limit, continuously reduce to a basis of the Schwarzian/Jackiw-Teitelboim functional space of gravitational fluctuations.

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arXiv2026

Why Indices Count the Total Number of Black Hole Microstates (at large N)

Using supersymmetric localization, we show that the partition function of four-dimensional superconformal gauge theories - computed as a trace over BPS states without the insertion of $(-1)^F$ - is perturbatively protected and piecewise independent of the gauge coupling. We derive a matrix-integral representation of this observable at $g_{\text{YM}}=0$ for generic four-dimensional superconformal gauge theories. For $U(N)$ maximally supersymmetric Yang-Mills theory we study such a matrix integral and show that, even at finite $N$, it localizes to ensembles of superconformal indices near its essential singularities. The latter asymptotic localization projects out any potential discontinuity of the perturbatively protected partition function from zero to strong coupling and explains why single microcanonical indices reproduce the growth of the total number of BPS states in co-dimension one regions of large charges, up to large oscillations due to the insertion of $(-1)^F$. To compute quantum corrections to entropy at finite $N$ and small charges, the correct observable is the perturbatively protected partition function, which by definition is a positive quantity. We propose and test an improvement of the Cardy-like method that allows us to identify and compute perturbatively exact expressions for the leading large-$N$ on-shell action of eigenvalue configurations that we call orbifold, dressed orbifold, and eigenvalue-instanton saddles. These are also saddle points of large-charge expansions at finite $N$. We test the conclusions obtained from such large-charge saddle-point analysis at $N=2$ using explicit Cauchy-residue evaluation.

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arXiv2025

Generalized Bethe expansions of superconformal indices

We show the existence of infinitely many Bethe expansions for general four dimensional superconformal theories. We then propose an analytic method to systematically obtain all the Bethe solutions, both isolated and continuous, for general superconformal theories. In particular, we show that the contribution from the continuous manifold of solutions to the index comes from isolated points on this manifold. We check our proposals on $\mathcal{N}=4$ SYM. For $U(3)$ or $SU(3)$, which are the first examples with continuous solutions, we demonstrate the non-trivial cancellation between the tachyon contributions from the previously known isolated solutions and those from the continuous solutions.

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arXiv2025

The Schwarzian from gauge theories

The continuum of holographic dual gravitational charges is recovered out of the discrete spectrum of $U(N)$ $\mathcal{N}=4$ SYM on $\mathbb{R}\times S^3\,$. In such a limit, the free energy of the free gauge theory is computed up to logarithmic contributions and exponentially suppressed contributions. Assuming the supergravity dual prediction to correctly capture strong-coupling results in field theory, the answer is bound to encode a complete low-temperature expansion of the Gibbons-Hawking gravitational on-shell action, valid well beyond the vicinity of supersymmetric black hole solutions. The formula recovers the long awaited Schwarzian contribution at low enough temperatures for certain choices of flows to the continuum. One such choice identifies the chemical potentials and thermodynamic charges in field theory with the chemical potentials and thermodynamic charges of the dual black holes. For such a flow the computed mass-gap kinematically matches the conjectured strong-coupling result obtained by Boruch, Heydeman, Iliesiu and Turiaci in supergravity, including small $1/λ$-corrections. The {emergent} reparameterizations, broken by the selection of the Schwarzian, correspond to redefinitions of the relevant cutoff scale. Observations are made regarding the existence of $\frac{1}{8}$-BPS black holes and how this is in tension with BPS inequalities. The RG-flow procedure leading to these results opens a way to understanding the emergence of chaos in gauge theories and its relation to non-extremal and non-supersymmetric black hole physics.

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arXiv2024

Large black hole entropy from the giant brane expansion

We show that the Bekenstein-Hawking entropy of large supersymmetric black holes in AdS$_5\times S^5$ emerges from remarkable cancellations in the giant graviton expansions recently proposed by Imamura, and Gaiotto and Lee, independently. A similar cancellation mechanism is shown to happen in the exact expansion in terms of free fermions recently put-forward by Murthy. These two representations can be understood as sums over independent systems of giant D3-branes and free fermions, respectively. At large charges, the free energy of each independent system localizes to its asymptotic expansion near the leading singularity. The sum over the independent systems maps their localized free energy to the localized free energy of the superconformal index of $U(N)$ $\mathcal{N}=4$ SYM. This result constitutes a non-perturbative test of the giant graviton expansion valid at any value of $N$. Moreover, in the holographic scaling limit $N\to\infty$ at fixed ratio $\frac{\text{Entropy}}{N^2}\,$, it recovers the 1/16 BPS black hole entropy by a saddle-point approximation of the giant graviton expansion.

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arXiv2024

Giant graviton expansion of Schur index and quasimodular forms

The flavored superconformal Schur index of $\mathcal N=4$ $U(N)$ SYM has finite $N$ corrections encoded in its giant graviton expansion in terms of D3 branes wrapped in $AdS_{5}\times S^{5}$. The key element of this decomposition is the non-trivial index of the theory living on the wrapped brane system. A remarkable feature of the Schur limit is that the brane index is an analytic continuation of the flavored index of $\mathcal N=4$ $U(n)$ SYM, where $n$ is the total brane wrapping number. We exploit recent exact results about the Schur index of $\mathcal N=4$ $U(N)$ SYM to evaluate the closed form of the the brane indices appearing in the giant graviton expansion. Away from the unflavored limit, they are characterized by quasimodular forms providing exact information at all orders in the index universal fugacity. As an application of these results, we present novel exact expressions for the giant graviton expansion of the unflavored Schur index in a class of four dimensional $\mathcal N=2$ theories with equal central charges $a=c$, i.e. the non-Lagrangian theories $\widehatΓ(SU(N))$ with $Γ= E_{6}, E_{7}, E_{8}$.

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arXiv2024

Large $N$ Schur index of $\mathcal N=4$ SYM from semiclassical D3 brane

We consider the refined Schur superconformal index of 4d $\mathcal N=4$ $U(N)$ SYM and the first term of its giant-graviton expansion, first predicted in arXiv:2001.11667 using indirect superconformal algebra considerations and analytic continuation of fugacities. This correction is the leading non-perturbative correction to the index at large $N$ and we reproduce it from the semiclassical partition function of quantum D3 brane wrapped on $S^{1}\times S^{3}$ in a twisted modification of the $AdS_{5}\times S^{5}$ string background, depending on the index R-symmetry fugacity. Our calculation does not exploit directly supersymmetry. It is based on the determination of the partition function of the various bosonic and fermionic fluctuations on the wrapped brane whose action is conformal with specific constant holonomies along thermal cycle. We show how those partition functions may be obtained by adapting the operator counting method of Cardy to the twisted background.

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arXiv2023

Thermodynamics of black holes with probe D-branes

Understanding how the thermodynamic properties of a black hole are modified when probed by D-branes is an important problem in AdS/CFT. This work focuses on a recently proposed black hole/D3-brane system in AdS$_5\times$S$^5$, which is dual to four-dimensional N=4 SYM in the presence of a two-dimensional surface defect. The Laplace transform that extracts the asymptotic growth of states in this defect CFT naturally defines a thermodynamic approach in the gravitational side of the duality for which charges and entropy are real. Studying the superconformal defect index in a large-charge expansion for all values of~$N$, we compute the leading correction to the entropy of the combined system, which matches precisely with its gravity counterpart.

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arXiv2023

Supersymmetric phases of AdS$_4$/CFT$_3$

We exhibit an infinite family of supersymmetric phases in the three-dimensional ABJM superconformal field theory and the dual asymptotically AdS$_4$ gravity. They are interpreted as partially deconfined phases which generalize the confined/pure AdS phase and deconfined/supersymmetric black hole phase. Our analysis involves finding a family of saddle-points of the superconformal index labelled by rational points (equivalently, roots of unity), separately in the bulk and boundary theories. In the ABJM theory we calculate the free energy of each saddle by the large-$N$ asymptotic expansion of the superconformal index to all orders in perturbation theory near the saddle-point. We find that this expansion terminates at finite order. In the gravitational theory we show that there is a corresponding family of solutions, constructed by orbifolding the eleven-dimensional uplift of the supersymmetric black hole. The on-shell gravitational action of each orbifold agrees with the free energy of the corresponding saddle in the SCFT. We find that there are two saddles in the ABJM theory with the same entropy as the supersymmetric black hole, corresponding to the two primitive fourth-roots of unity, which causes macroscopic oscillations in the microcanonical index.

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arXiv2023

On the brane expansion of the Schur index

We consider the Schur index of $\mathcal N=4$ $U(N)$ SYM theory in 4d and its holographic giant graviton-type expansion at finite $N$. We compute the world-volume brane superconformal index by a recently proposed definition of the gauge holonomy integral as a multivariate residue. This is evaluated by a novel deformation algorithm that avoids Gröbner basis methods. Various terms of the brane expansion are computed and shown to be free of wall-crossing singularities to the order we explored. The relation between the brane expansion and previous giant graviton-type represenations of the Schur index is clarified.

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arXiv2023

$1/N$ expansion of the D3-D5 defect CFT

We consider four dimensional $U(N)$ $\mathcal N=4$ SYM theory interacting with a 3d $\mathcal N=4$ theory living on a codimension-one interface and holographically dual to the D3-D5 system without flux. Localization captures several observables in this dCFT, including its free energy, related to the defect expectation value, and single trace $\frac{1}{2}$-BPS composite scalars. These quantities may be computed in a hermitian one-matrix model with non-polynomial single-trace potential. We exploit the integrable Volterra hierarchy underlying the matrix model and systematically study its $1/N$ expansion at any value of the 't Hooft coupling. In particular, the strong coupling regime is determined -- up to non-perturbative exponentially suppressed corrections -- by differential relations that constrain higher order terms in the $1/N$ expansion. The analysis is extended to the model with $SU(N)$ gauge symmetry by resorting to the more general Toda lattice equations.

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arXiv2022

On the 4d superconformal index near roots of unity: Bulk and Localized contributions

We study the expansion near roots of unity of the superconformal index of 4d $SU(N)$ $\mathcal{N}=4$ SYM. In such an expansion, middle-dimensional walls of non-analyticity are shown to emerge in the complex analytic extension of the integrand. These walls intersect the integration contour at infinitesimal vicinities and come from both, the vector and chiral multiplet contributions, and combinations thereof. We will call these intersections vector and chiral bits, and the complementary region bulk, and show that, in the corresponding limit, the integrals along the infinitesimal bits include, among other contributions, factorized products of either Chern-Simons and 3d topologically twisted partition functions. In particular, we find that the leading asymptotic contribution to the index, which comes from collecting all contributions coming from vector bits, reduces to an average over a set of $N$ copies of three-dimensional $SU(N)$ Chern-Simons partition functions in Lens spaces $L(m,1)$ with $m>1\,$, in the presence of background $\mathbb{Z}^{N-1}_m$ flat connections. The average is taken over the background connections, which are the positions of individual vector bits along the contour. We also find there are other subleading contributions, a finite number of them at finite $N$, which include averages over products of Chern-Simons and/or topologically $A$-twisted Chern-Simons-matter partition functions in three-dimensional manifolds. This shows how in certain limits the index of 4d $SU(N)$ $\mathcal{N}=4$ SYM organizes, via an unambiguously defined coarse graining procedure, into averages over a finite number of lower dimensional theories.

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arXiv2022

Quantum Phases of $4d$ $SU(N)$ $\mathcal{N}=4$ SYM

It is argued that $4d$ $SU(N)$ $\mathcal{N}=4$ SYM has an accumulation line of zero-temperature topologically ordered phases. Each of these phases corresponds to $N$ bound states charged under electromagnetic $\mathbb{Z}^{(1)}_N$ one-form symmetries. Each of the $N$ bound states is made of two Dyonic flux components each of them extended over a two dimensional surface. They are localized at the fixed loci of a rotational action, and are argued to correspond to conformal blocks (or primaries) of an $SU(N)_1$ WZNW model on a two-torus.

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arXiv2021

The asymptotic growth of states of the 4d N=1 superconformal index

We show that the superconformal index of N=1 superconformal field theories in four dimensions has an asymptotic growth of states which is exponential in the charges. Our analysis holds in a Cardy-like limit of large charges, for which the index is dominated by small values of chemical potentials. In this limit we find the saddle points of the integral that defines the superconformal index using two different methods. One method, valid for finite N, is to first take the Cardy-like limit and then find the saddle points. The other method is to analyze the saddle points at large N and then take the Cardy-like limit. The result of both analyses is that the asymptotic growth of states of the superconformal index exactly agrees with the Bekenstein-Hawking entropy of supersymmetric black holes in the dual AdS$_5$ theory.

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arXiv2021

Supersymmetric phases of 4d N=4 SYM at large N

We find a family of complex saddle-points at large N of the matrix model for the superconformal index of SU(N) N=4 super Yang-Mills theory on $S^3 \times S^1$ with one chemical potential $τ$. The saddle-point configurations are labelled by points $(m,n)$ on the lattice $Λ_τ= \mathbb{Z} τ+\mathbb{Z}$ with $\text{gcd}(m,n)=1$. The eigenvalues at a given saddle are uniformly distributed along a string winding $(m,n)$ times along the $(A,B)$ cycles of the torus $\mathbb{C}/Λ_τ$. The action of the matrix model extended to the torus is closely related to the Bloch-Wigner elliptic dilogarithm, and the related Bloch formula allows us to calculate the action at the saddle-points in terms of real-analytic Eisenstein series. The actions of $(0,1)$ and $(1,0)$ agree with that of pure AdS$_5$ and the supersymmetric AdS$_5$ black hole, respectively. The black hole saddle dominates the canonical ensemble when $τ$ is close to the origin, and there are new saddles that dominate when $τ$ approaches rational points. The extension of the action in terms of modular forms leads to a simple treatment of the Cardy-like limit $τ\to 0$.

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arXiv2020

From multi-gravitons to Black holes: The role of complex saddles

By applying the Atiyah-Bott-Berline-Vergne equivariant integration formula upon double dimensional integrals, we find a way to compute the matrix integral representations of $4d$ $\mathcal{N}=1$ superconformal indices. The final formula allows us to easily extract analytic results in the large-rank expansion of certain theories. As an example, we compute the leading one-loop corrections to the effective action of the known complex saddles in those theories. For a superconformal index of $SU(N)$ $\mathcal{N}=4$ SYM, we use the equivariant integration formula and the Picard-Lefschetz method to show that at large enough values of $N$, only two, among the known complex saddles, dominate the counting of large operators i.e. of operators with charges of order $N^2$. Contributions from other known complex saddles are present, but we show they are exponentially suppressed in that range of charges; the smaller the charges the less suppressed they are, and eventually, to count small operators i.e. operators with charges smaller than $N^{2/3}$, like multi-gravitons, they can not be neglected.

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arXiv2020

The large-$N$ limit of the 4d $\mathcal{N}=1$ superconformal index

We systematically analyze the large-$N$ limit of the superconformal index of $\mathcal{N}=1$ superconformal theories having a quiver description. The index of these theories is known in terms of unitary matrix integrals, which we calculate using the recently-developed technique of elliptic extension. This technique allows us to easily evaluate the integral as a sum over saddle points of an effective action in the limit where the rank of the gauge group is infinite. For a generic quiver theory under consideration, we find a special family of saddles whose effective action takes a universal form controlled by the anomaly coefficients of the theory. This family includes the known supersymmetric black hole solution in the holographically dual AdS$_5$ theories. We then analyze the index refined by turning on flavor chemical potentials. We show that, for a certain range of chemical potentials, the effective action again takes a universal cubic form that is controlled by the anomaly coefficients of the theory. Finally, we present a large class of solutions to the saddle-point equations which are labelled by group homomorphisms of finite abelian groups of order $N$ into the torus.

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arXiv2019

Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS$_{\bf 5}$ black holes

We present a holographic derivation of the entropy of supersymmetric asymptotically AdS$_5$ black holes. We define a BPS limit of black hole thermodynamics by first focussing on a supersymmetric family of complexified solutions and then reaching extremality. We show that in this limit the black hole entropy is the Legendre transform of the on-shell gravitational action with respect to three chemical potentials subject to a constraint. This constraint follows from supersymmetry and regularity in the Euclidean bulk geometry. Further, we calculate, using localization, the exact partition function of the dual $\mathcal{N}=1$ SCFT on a twisted $S^1\times S^3$ with complexified chemical potentials obeying this constraint. This defines a generalization of the supersymmetric Casimir energy, whose Legendre transform at large $N$ exactly reproduces the Bekenstein-Hawking entropy of the black hole.

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