arXiv subjects

Giorgos Eleftheriou

Publications and source records attributed to Giorgos Eleftheriou.

5 recordsLinked to original sources

arXiv2026

Fermionic trace relations and supersymmetric indices at finite $N$

We study invariants of bosonic and fermionic (Grassmann-valued) matrices under the adjoint action of $U(N)$, weighted by the fermion number. Such models naturally appear as the supersymmetric indices of supersymmetric gauge theories and are captured by $U(N)$ matrix models. We discuss two features of the fermionic models that are qualitatively different from bosonic models. Firstly, the $2N^\text{th}$ power of a Grassmann matrix vanishes, which gives rise to many new trace relations. Secondly, trace relations in models involving fermions could cause an increase in the supersymmetric index as $N$ decreases, in contrast with purely bosonic models. We focus on a simple model involving one fermion and one derivative that corresponds to a $\frac14$-BPS supersymmetric index in $\mathcal{N}=4$ SYM theory, in which we find that the index is independent of $N$. We prove this rank-independence analytically, and experimentally study the cancellations between bosonic and fermionic trace relations that lead to it. Based on these observations, we make some conjectures on resulting algebraic structures, including the analogue of the polarized Cayley-Hamilton identities and the Second Fundamental Theorem of invariants in the presence of Grassmann matrices. Finally, we present various (smooth and singular) limits of the most general supersymmetric index in $\mathcal{N}=4$ SYM theory, and study some patterns in their behavior as a function of $N$.

hep-th↗

arXiv2025

Localization and wall-crossing of giant graviton expansions in AdS$_5$

The $\frac12$-BPS indices of $\mathcal{N}=4$ Super Yang-Mills theory with unitary, orthogonal, and symplectic groups all admit $q$-expansions suggesting an interpretation in terms of D-branes in the dual bulk AdS$_5$ string theories. We present a derivation of these expansions in the corresponding bulk duals by quantizing the moduli space of $\frac12$-BPS giant gravitons using supersymmetric localization, extending and clarifying our study in arxiv:2312.14921. We perform a detailed analysis of the one-loop fluctuations around the maximal giants (the fixed points), and show how the Hamiltonian analysis is recovered from the functional integral for the equivariant index. We show that the analytic continuation for these giant graviton expansions observed in the literature maps precisely to a wall-crossing phenomenon for the index. In the case of orthogonal and symplectic gauge groups, the $\mathbb{Z}_2$ quotient in the bulk leads to a corresponding projection in the $q$-expansion. Additional terms in the expansion related to the Pfaffian operator arise from topologically stable branes in the bulk dual on AdS$_5 \times \mathbb{RP}^5$.

hep-th↗

arXiv2024

The giant graviton expansion in $AdS_5 \times S^5$

The superconformal index of $\frac12$-BPS states of $N=4$ U(N) super Yang-Mills theory has a known infinite $q$-series expression with successive terms suppressed by $q^N$. We derive a holographic bulk interpretation of this series by evaluating the corresponding functional integral in the dual $AdS_5 \times S^5$. The integral localizes to a product of small fluctuations of the vacuum and of the collective modes of an arbitrary number of giant-gravitons wrapping an $S^3$ of maximal size inside the $S^5$. The quantum mechanics of the small fluctuations of one maximal giant is described by a supersymmetric version of the Landau problem. The quadratic fluctuation determinant reduces to a sum over the supersymmetric ground states, and precisely reproduces the first non-trivial term in the infinite series. Further, we show that the terms corresponding to multiple giants are obtained precisely by the matrix versions of the above super-quantum-mechanics.

hep-th↗

arXiv2023

Root of unity asymptotics for Schur indices of 4d Lagrangian theories

The Schur index of a $4$ dimensional $\mathcal{N}=2$ superconformal field theory counts (with sign) bosonic and fermionic states that preserve $4$ supercharges. We consider the Schur indices of $4$d $\mathcal{N}=4$ super Yang-Mills and $\mathcal{N}=2$ circular quiver gauge theories with gauge groups $U(N)$ or $SU(N)$. We calculate the exponentially dominant part of their asymptotic expansions as the index parameter $q$ approaches any root of unity. We find that some of the indices exhibit ``small" ($\mathcal{O}(N^0)$ as $N \rightarrow \infty$) exponential growth, which is much smaller than an $\mathcal{O}(N^2)$ exponential growth of states that is indicative of a black hole. This implies that the indices do not capture a growth of states that would correspond to a supersymmetric black hole that preserves 4 supercharges in the holographic dual AdS theory. Interestingly, the exponentially dominant part in the Schur asymptotics we consider, depends on the parity of the rank $N$.

hep-th↗

arXiv2020

Supersymmetry anomalies and the Wess-Zumino Model in a supergravity background

We briefly recall the procedure for computing the Ward Identities in the presence of a regulator which violates the symmetry being considered. We compute the first non-trivial correction to the supersymmetry Ward Identity of the Wess-Zumino model in the presence of background supergravity using dimensional regularisation. We find that the result can be removed using a finite local counter term and so there is no supersymmetry anomaly.

hep-th↗