arXiv subjects

Alfredo González Lezcano

Publications and source records attributed to Alfredo González Lezcano.

11 recordsLinked to original sources

arXiv2026

The giant graviton expansion in AdS$_5\times$SE$_5$

We study giant graviton-like D3-branes as probe configurations in type IIB supergravity backgrounds AdS$_5\times$SE$_5$, with emphasis on the structure of the five-dimensional Sasaki-Einstein manifolds SE$_5$. These configurations wrap supersymmetric three-cycles in SE$_5$ and rotate at the speed of light along the Reeb direction. We formulate the general problem in terms of the transverse Kähler potential and show that configurations carrying maximal angular momentum can be described by loci where the transverse Kähler potential diverges in suitably chosen coordinates. We quantize a particular set of excitations, similar to those considered in the AdS$_5\times S^5$ case, and show that they are governed by a Fock-Darwin problem with a conical deficit, which generalizes the Landau problem obtained for $S^5$. Succinctly, the information about the geometry of SE$_5$ is encoded in the form of the external potential and the conical deficit. We compute a protected contribution to the superconformal index arising from quantized fluctuations of supersymmetric giant graviton configurations. For the explicit case of AdS$_5\times T^{1,1}$, we recover the finite-$N$ protected index of the dual quiver ${\cal N}=1$ superconformal field theory in the sector captured by a non-Abelian generalization of the quantized degrees of freedom.

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arXiv2024

Supersymmetric spectrum for vector multiplet on Euclidean AdS$_2$

Quantum study of supersymmetric theories on Euclidean two dimensional anti-de Sitter space (EAdS$_2$) requires complexified spectrum. For a chiral multiplet, we showed that the spectrum of the Dirac operator acquires a universal shift of $\text{i}/2$ from the real spectrum to make the supersymmetry between boson and fermion manifest, where both the bosonic and fermionic eigenfunctions are normalizable using an appropriate definition of Euclidean inner product. We extend this analysis to the vector multiplet, where we show that the gaugino requires both $+\text{i}/2$ and $-\text{i}/2$ shift from the real spectrum, and there is additional isolated point at vanishing spectral parameter which is mapped by supersymmetry to the boundary zero modes of the vector field. Furthermore, this spectral analysis shows that not every bosonic fields in the vector multiplet can satisfy normalizable boundary condition. Nevertheless, aided by a reorganization of fields into a cohomological form, we find the supersymmetry mapping between bosons and fermions in terms of the expansion coefficients with respect to the newly constructed basis.

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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

Supersymmetry and complexified spectrum on Euclidean AdS$_2$

Quantum study of supersymmetric theories on Euclidean two dimensional anti-de Sitter space (AdS$_2$) is invalid if we use the standard normalizable functional basis due to its incompatibility with supersymmetry. We cure this problem by demonstrating that supersymmetry requires complexified spectrum and constructing the supersymmetric basis for scalar and spinor fields. Our new basis is free of fermionic zero modes, delta-function normalizable with respect to a newly defined inner product, and compatible with the supersymmetric asymptotic boundary condition. We also explore the one-loop evaluation using this basis and show that it agrees with the standard nonsupersymmetric basis up to a global contribution arising from the fermion zero mode.

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arXiv2023

Supersymmetric localization: ${\cal N}=(2,2)$ theories on S$^2$ and AdS$_2$

Application of the supersymmetric localization method to theories on anti-de Sitter spacetime has received recent interest, yet still remains as a challenging problem. In this paper, we focus on (global) Euclidean AdS$_2$, on which we consider an Abelian ${\cal N}=(2,2)$ theory and implement localization computation to obtain the exact partition function. For comparison, we also revisit the theory on S$^2$ and perform a parallel computation. We refine the notion of equivariant supersymmetry and use appropriate functional integration measure. For AdS$_2$ we choose a supersymmetric boundary condition which is compatible with the principle of variation. To evaluate the 1-loop determinant about the localization saddle, we use index theory and fixed point formula, where we pay attention to the effect of zero modes and their superpartners. The existence of fermionic superpartner of 1-form boundary zero modes is proven. Obtaining the 1-loop determinant requires expansion of the index that presents an ambiguity, which we resolve using boundary condition. The resulting partition function reveals an overall dependence on the size of the background manifold, AdS$_2$ as well as S$^2$, as a sum of two types of contributions: a local one from local conformal anomaly through the index computation and a global one coming from zero modes. This overall size dependence is confirmed by the perturbative 1-loop evaluation using heat kernel method.

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arXiv2022

Cardy Expansion of 3d Superconformal Indices and Corrections to the Dual Black Hole Entropy

We consider the superconformal index of three-dimensional ${\cal N}=2$ supersymmetric field theories computed via localization on $S^1\times S^2$. We systematically develop an expansion where the ratio of the radius of $S^1$ to the radius of $S^2$ is taken very small -- a Cardy-like expansion. We emphasize the sub-leading structures in this Cardy-like expansion as well as their interplay with the large-$N$ limit for theories with gauge group of the form product of $U(N)$ factors. We demonstrate that taking the large-$N$ limit first leads to an expression for the index that only includes terms proportional to $1/β$ and powers of $β^{i=0,1,2}$ where $β$ is the ratio of radii. As we depart from the $β\to 0$ limit for finite $N$, we find indications of non-perturbative contributions of the form $e^{-1/β}$. For the ABJM theory we explore the implications of the Cardy-like expansion for corrections to the entropy of the rotating, electricallly charged, asymptotically AdS$_4$ dual black hole. Interestingly, we find that the corrections in $β$ to the entropy can be accounted for by appropriately shifting the electric charges and the angular momentum

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arXiv2022

$c$-Functions in Flows Across Dimensions

We explore the notion of $c$-functions in renormalization group flows between theories in different spacetime dimensions. We discuss functions connecting central charges of the UV and IR fixed point theories on the one hand, and functions which are monotonic along the flow on the other. First, using the geometric properties of the holographic dual RG flows across dimensions and the constraints from the null energy condition, we construct a monotonic holographic $c$-function and thereby establish a holographic $c$-theorem across dimensions. Second, we use entanglement entropies for two different types of entangling regions in a field theory along the RG flow across dimensions to construct candidate $c$-functions which satisfy one of the two criteria but not both. In due process we also discuss an interesting connection between corner contributions to the entanglement entropy and the topology of the compact internal space. As concrete examples for both approaches, we holographically study twisted compactifications of 4d $\mathcal N=4$ SYM and compactifications of 6d $\mathcal N=(2,0)$ theories.

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arXiv2022

Logarithmic Corrections to the Entropy of Rotating Black Holes and Black Strings in AdS$_5$

We investigate logarithmic corrections to the entropy of supersymmetric, rotating, asymptotically AdS$_5$ black holes and black strings. Within the framework of the AdS/CFT correspondence, the entropy of these black objects is determined, on the field theory side, by the superconformal index and the refined topologically twisted index of $\mathcal{N}=4$ supersymmetric Yang-Mills theory, respectively. We read off the logarithmic correction from those field-theoretic partition functions. On the gravity side, we take the near-horizon limit and apply the Kerr/CFT correspondence whose associated charged Cardy formula describes the degeneracy of states at subleading order and determines the logarithmic correction to the entropy. We find perfect agreement between these two approaches. Our results provide a window into precision microstate counting and demonstrate the efficacy of low-energy, symmetry-based approaches such as the Kerr/CFT correspondence for asymptotically AdS black objects under certain conditions.

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arXiv2021

Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions

We systematically study various sub-leading structures in the superconformal index of ${\cal N}=4$ supersymmetric Yang-Mills theory with SU($N$) gauge group. We concentrate in the superconformal index description as a matrix model of elliptic gamma functions and in the Bethe-Ansatz presentation. Our saddle-point approximation goes beyond the Cardy-like limit and we uncover various saddles governed by a matrix model corresponding to SU($N$) Chern-Simons theory. The dominant saddle, however, leads to perfect agreement with the Bethe-Ansatz approach. We also determine the logarithmic correction to the superconformal index to be $\log N$, finding precise agreement between the saddle-point and Bethe-Ansatz approaches in their respective approximations. We generalize the two approaches to cover a large class of 4d ${\cal N}=1$ superconformal theories. We find that also in this case both approximations agree all the way down to a universal contribution of the form $\log N$. The universality of this last result constitutes a robust signature of this ultraviolet description of asymptotically AdS$_5$ black holes and could be tested by low-energy IIB supergravity.

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arXiv2021

The Bethe-Ansatz approach to the $\mathcal N=4$ superconformal index at finite rank

We investigate the Bethe-Ansatz (BA) approach to the superconformal index of ${\cal N}=4$ supersymmetric Yang-Mills with SU($N$) gauge group in the context of finite rank, $N$. We explicitly explore the role of the various types of solutions to the Bethe-Ansatz Equations (BAE) in recovering the exact index for $N=2,3$. We classify the BAE solutions as standard (corresponding to a freely acting orbifold $T^2/\mathbb{Z}_m \times \mathbb{Z}_n$) and non-standard. For $N=2$, we find that the index is fully recovered by standard solutions and displays an interesting pattern of cancellations. However, for $N\ge 3$, the standard solutions alone do not suffice to reconstruct the index. We present quantitative arguments in various regimes of fugacities that highlight the challenging role played by the continuous families of non-standard solutions.

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arXiv2020

Microstate Counting via Bethe Ansätze in the 4d ${\cal N}=1$ Superconformal Index

We study the superconfomal index of four-dimensional toric quiver gauge theories using a Bethe Ansatz approach recently applied by Benini and Milan. Relying on a particular set of solutions to the corresponding Bethe Ansatz equations we evaluate the superconformal index in the large $N$ limit, thus avoiding to take any Cardy-like limit. We present explicit results for theories arising as a stack of $N$ D3 branes at the tip of toric Calabi-Yau cones: the conifold theory, the suspended pinch point gauge theory, the first del Pezzo theory and $Y^{p,q}$ quiver gauge theories. For a suitable choice of the chemical potentials of the theory we find agreement with predictions made for the same theories in the Cardy-like limit. However, for other regions of the domain of chemical potentials the superconformal index is modified and consequently the associated black hole entropy receives corrections. We work out explicitly the simple case of the conifold theory.

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