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We study the superconformal index of 3d $\mathcal{N}=2$ superconformal field theories on $S^1\times_{\omega} S^2$ in the Cardy-like limit where the radius of the $S^1$ is much smaller than that of the $S^2$. We show that the first two leading terms in this Cardy-like expansion are dictated by the Bethe Ansatz formulation of the topologically twisted index of the same theory. We apply this relation to 3d $\mathcal{N}=2$ holographic superconformal field theories describing the low-energy dynamics of $N$ M2-branes and derive closed form expressions, valid to all orders in the $1/N$ expansion, for the two leading terms in the Cardy-like expansion of the superconformal index. We also discuss the implications of our results for the entropy of supersymmetric Kerr-Newman black holes in AdS$_4$ and the four-derivative corrections to 4d gauged supergravity., Comment: v1: 31 pages + appendices

This paper presents a novel approach to Autonomous Vehicle (AV) control through the application of active inference, a theory derived from neuroscience that conceptualizes the brain as a predictive machine. Traditional autonomous driving systems rely heavily on Modular Pipelines, Imitation Learning, or Reinforcement Learning, each with inherent limitations in adaptability, generalization, and computational efficiency. Active inference addresses these challenges by minimizing prediction error (termed "surprise") through a dynamic model that balances perception and action. Our method integrates active inference with deep learning to manage lateral control in AVs, enabling them to perform lane following maneuvers within a simulated urban environment. We demonstrate that our model, despite its simplicity, effectively learns and generalizes from limited data without extensive retraining, significantly reducing computational demands. The proposed approach not only enhances the adaptability and performance of AVs in dynamic scenarios but also aligns closely with human-like driving behavior, leveraging a generative model to predict and adapt to environmental changes. Results from extensive experiments in the CARLA simulator show promising outcomes, outperforming traditional methods in terms of adaptability and efficiency, thereby advancing the potential of active inference in real-world autonomous driving applications., Comment: The work is partly supported by a sponsor. Authors need to complete the final report submission before any type of publication according to the sponsor. The final report will be submitted in few weeks. Then, authors will reinstate this paper after that

Cybersecurity breaches in digital substations can pose significant challenges to the stability and reliability of power system operations. To address these challenges, defense and mitigation techniques are required. Identifying and detecting anomalies in information and communication technology (ICT) is crucial to ensure secure device interactions within digital substations. This paper proposes a task-oriented dialogue (ToD) system for anomaly detection (AD) in datasets of multicast messages e.g., generic object oriented substation event (GOOSE) and sampled value (SV) in digital substations using large language models (LLMs). This model has a lower potential error and better scalability and adaptability than a process that considers the cybersecurity guidelines recommended by humans, known as the human-in-the-loop (HITL) process. Also, this methodology significantly reduces the effort required when addressing new cyber threats or anomalies compared with machine learning (ML) techniques, since it leaves the models complexity and precision unaffected and offers a faster implementation. These findings present a comparative assessment, conducted utilizing standard and advanced performance evaluation metrics for the proposed AD framework and the HITL process. To generate and extract datasets of IEC 61850 communications, a hardware-in-the-loop (HIL) testbed was employed., Comment: 10 pages, 10 figures, Submitted to IEEE Transactions on Information Forensics and Security

We investigate the 3-sphere partition functions of various 3d $\mathcal{N}=2$ holographic SCFTs arising from the $N$ stack of M2-branes in the 't Hooft limit both analytically and numerically. We first employ a saddle point approximation to evaluate the free energy $F=-\log Z$ at the planar level, tracking the first subleading corrections in the large 't Hooft coupling $\lambda$ expansion. Subsequently, we improve these results by determining the planar free energy to all orders in the large $\lambda$ expansion via numerical analysis. Remarkably, the resulting planar free energies turn out to take a universal form, supporting a prediction that these $S^3$ partition functions are all given in terms of an Airy function even beyond the special cases where the Airy formulae were derived analytically in the literature; in this context we also present new Airy conjectures in several examples. The subleading behaviors we captured encode a part of quantum corrections to the M-theory path integrals around dual asymptotically Euclidean AdS$_4$ backgrounds with the corresponding internal manifolds through holographic duality., Comment: v1: 46 pages + appendices; v2: minor revisions and references added

We study the logarithmic corrections to various CFT partition functions in the context of the AdS$_4$/CFT$_3$ correspondence for theories arising on the worldvolume of M2-branes. We utilize four-dimensional gauged supergravity and heat kernel methods and present general expressions for the logarithmic corrections to the gravitational on-shell action and black hole entropy for a number of different supergravity backgrounds. We outline several subtle features of these calculations and contrast them with a similar analysis of logarithmic corrections performed directly in the eleven-dimensional uplift of a given four-dimensional supergravity background. We find results consistent with AdS/CFT provided that the infinite sum over KK modes on the internal space is regularized in a specific manner. This analysis leads to an explicit expression for the logarithmic correction to the Bekenstein-Hawking entropy of large Kerr-Newmann and Reissner-Nordstr\"om black holes in AdS$_4$. Our results also have important implications for effective field theory coupled to gravity in AdS$_4$ and for the existence of scale-separated AdS$_4$ vacua in string theory, which come in the form of new constraints on the field content and mass spectrum of matter fields., Comment: v1: 87 pages, 10 tables; v2: Seeley-de Witt coefficients in the presence of non-minimal couplings dictated by supersymmetry are newly addressed in section 5 and following places

As Information and Communication Technology (ICT) equipment continues to be integrated into power systems, issues related to cybersecurity are increasingly emerging. Particularly noteworthy is the transition to digital substations, which is shifting operations from traditional hardwired-based systems to communication-based Supervisory Control and Data Acquisition (SCADA) system operations. These changes in the power system have increased the vulnerability of the system to cyber-attacks and emphasized its importance. This paper proposes a machine learning (ML) based post event analysis of the power system in order to respond to these cybersecurity issues. An artificial neural network (ANN) and other ML models are trained using transient fault measurements and cyber-attack data on substations. The trained models can successfully distinguish between power system faults and cyber-attacks. Furthermore, the results of the proposed ML-based methods can also identify 10 different fault types and the location where the event occurred., Comment: Submitted to 2024 IEEE Power and Energy Society General Meeting

In recent years, critical infrastructure and power grids have experienced a series of cyber-attacks, leading to temporary, widespread blackouts of considerable magnitude. Since most substations are unmanned and have limited physical security protection, cyber breaches into power grid substations present a risk. Nowadays, software-defined network (SDN), a popular virtual network technology based on the OpenFlow protocol is being widely used in the substation automation system. However, the susceptibility of SDN architecture to cyber-attacks has exhibited a notable increase in recent years, as indicated by research findings. This suggests a growing concern regarding the potential for cybersecurity breaches within the SDN framework. In this paper, we propose a hybrid intrusion detection system (IDS)-integrated SDN architecture for detecting and preventing the injection of malicious IEC 61850-based generic object-oriented substation event (GOOSE) messages in a digital substation. Additionally, this program locates the fault's location and, as a form of mitigation, disables a certain port. Furthermore, implementation examples are demonstrated and verified using a hardware-in-the-loop (HIL) testbed that mimics the functioning of a digital substation., Comment: 5 pages, 6 figures, 1 table, conference paper, supported by DOE (CESER) program

Cybersecurity breaches targeting electrical substations constitute a significant threat to the integrity of the power grid, necessitating comprehensive defense and mitigation strategies. Any anomaly in information and communication technology (ICT) should be detected for secure communications between devices in digital substations. This paper proposes large language models (LLM), e.g., ChatGPT, for the cybersecurity of IEC 61850-based digital substation communications. Multicast messages such as generic object oriented system event (GOOSE) and sampled value (SV) are used for case studies. The proposed LLM-based cybersecurity framework includes, for the first time, data pre-processing of communication systems and human-in-the-loop (HITL) training (considering the cybersecurity guidelines recommended by humans). The results show a comparative analysis of detected anomaly data carried out based on the performance evaluation metrics for different LLMs. A hardware-in-the-loop (HIL) testbed is used to generate and extract dataset of IEC 61850 communications., Comment: 5 pages, 2 figures, Accepted, 2024 IEEE Power & Energy Society General Meeting (PESGM), Seattle, WA, USA

We use holography in conjunction with recent results from supersymmetric localization to compute certain thermal observables for 3d $\mathcal{N}=2$ holographic SCFTs arising on the worldvolume of $N$ M2-branes. We obtain results for the thermal free energy density on $S^1 \times \mathbb{R}^2$, the Casimir energy on $T^{2} \times \mathbb{R}$, and the three leading coefficients in the large temperature limit of the free energy on $S^1\times S^2$ valid to subleading order in the large $N$ limit. As a byproduct of our holographic analysis we also present a conjecture for the structure of the large temperature expansion of the thermal free energy of general 3d CFTs on $S^1\times S^2$., Comment: 22 pages

We construct a general asymptotically locally AdS$_7$ stationary black hole solution of 7d maximal gauged supergravity with three angular momenta and two electric charges. When embedded in 11d supergravity the black hole describes the backreaction of $N$ coincident rotating M5-branes. We study the thermodynamic properties of the black hole and present explicit expressions for its entropy, energy, electric charges, and angular momenta. We show that in the supersymmetric limit of the solution its entropy and on-shell action precisely agree with the result for the path integral of the holographically dual 6d $\mathcal{N}=(2,0)$ SCFT on $S^1\times S^5$ to leading order in the large $N$ limit., Comment: v1: 32 pages; v2: minor revisions including corrected typos, attached a Mathematica Notebook providing various expressions in the paper

We study the $S^1\times\Sigma_{\mathfrak g}$ topologically twisted index and the squashed sphere partition function of various 3d $\mathcal N\geq2$ holographic superconformal field theories arising from M2-branes. Employing numerical techniques in combination with well-motivated conjectures we provide compact closed-form expressions valid to all orders in the perturbative $1/N$ expansion for these observables. We also discuss the holographic implications of our results for the topologically twisted index for the dual M-theory Euclidean path integral around asymptotically AdS$_4$ solutions of 11d supergravity. In Lorentzian signature this leads to a prediction for the corrections to the Bekenstein-Hawking entropy of a class of static asymptotically AdS$_4$ BPS black holes., Comment: v1: p.57; v2: minor revisions; v3: minor typos corrected

Safe and secure electric vehicle charging stations (EVCSs) are important in smart transportation infrastructure. The prevalence of EVCSs has rapidly increased over time in response to the rising demand for EV charging. However, developments in information and communication technologies (ICT) have made the cyber-physical system (CPS) of EVCSs susceptible to cyber-attacks, which might destabilize the infrastructure of the electric grid as well as the environment for charging. This study suggests a 5Ws \& 1H-based investigation approach to deal with cyber-attack-related incidents due to the incapacity of the current investigation frameworks to comprehend and handle these mishaps. Also, a stochastic anomaly detection system (ADS) is proposed to identify the anomalies, abnormal activities, and unusual operations of the station entities as a post cyber event analysis., Comment: 5 Pages, 2 Figures, 2 Tables, 10 Mathematical Equations, PES GM Conference Paper

We calculate quantum corrections to the entropy of four-dimensional de Sitter space induced by higher-derivative terms in the gravitational action and by one-loop effects. Employing the intertwinement in semiclassical gravity of Euclidean de Sitter and anti-de Sitter saddles, we embed effective de Sitter gravity theories in M-theory and express the entropy in terms of the regularized Euclidean anti-de Sitter action on an auxiliary $\mathrm{EAdS}_4 \times S^7/\mathbb{Z}_k$ background. We conjecture that the partition function of the holographically dual 3d ABJM CFT determines the explicit form of the corrections to the de Sitter entropy. This includes a logarithmic term, the coefficient of which, we show, agrees with an independent one-loop calculation around the $-S^4 \times S^7/\mathbb{Z}_k$ Euclidean de Sitter saddle. This provides evidence that the microscopic degrees of freedom behind the entropy of four-dimensional de Sitter space in gravitational theories with a holographic dual description are encapsulated by the path integral of the Euclidean CFT on the three-sphere., Comment: 11 pages; v2: additional comments included

We study a limit of the superconformal index of the ABJM theory on $S^1\times S^2$ in which the size of the circle is much smaller than the radius of the two-sphere. We derive closed form expressions for the two leading terms in this Cardy-like limit which are valid to all orders in the $1/N$ expansion. These results are facilitated by a judicious rewriting of the superconformal index which establishes a connection with the Bethe Ansatz Equations that control the topologically twisted index. Using the same technique we extend these results to the superconformal index of another holographic theory: 3d $\mathcal{N}=4$ SYM coupled to one adjoint and $N_f$ fundamental hypermultiplets. We discuss the implications of our results for holography and the physics of charged rotating black holes in AdS$_4$., Comment: v1: 40 pages; v2: minor revisions; v3: references updated; v4: added footnote 3, 4 and 10, references updated

We study the large $N$ limit of some supersymmetric partition functions of the $\mathrm{U}(N)_{k}\times \mathrm{U}(N)_{-k}$ ABJM theory computed by supersymmetric localization. We conjecture an explicit expression, valid to all orders in the large $N$ limit, for the partition function on the $\mathrm{U}(1)\times \mathrm{U}(1)$ invariant squashed sphere in the presence of real masses in terms of an Airy function. Several non-trivial tests of this conjecture are presented. In addition, we derive an explicit compact expression for the topologically twisted index of the ABJM theory valid at fixed $k$ to all orders in the $1/N$ expansion. We use these results to derive the topologically twisted index and the sphere partition function in the 't Hooft limit which correspond to genus $\tt g$ type IIA string theory free energies to all orders in the $\alpha'$ expansion. We discuss the implications of our results for holography and the physics of AdS$_4$ black holes., Comment: v1: 56 pages, 4 figures; v2: corrected typos in equations (2.5) and (4.69), updated references; v3: added footnote 11, minor revisions in Subsection 4.4; v4: minor typos corrected

Safe and reliable electric vehicle charging stations (EVCSs) have become imperative in an intelligent transportation infrastructure. Over the years, there has been a rapid increase in the deployment of EVCSs to address the upsurging charging demands. However, advances in information and communication technologies (ICT) have rendered this cyber-physical system (CPS) vulnerable to suffering cyber threats, thereby destabilizing the charging ecosystem and even the entire electric grid infrastructure. This paper develops an advanced cybersecurity framework, where STRIDE threat modeling is used to identify potential vulnerabilities in an EVCS. Further, the weighted attack defense tree approach is employed to create multiple attack scenarios, followed by developing Hidden Markov Model (HMM) and Partially Observable Monte-Carlo Planning (POMCP) algorithms for modeling the security attacks. Also, potential mitigation strategies are suggested for the identified threats., Comment: 5 pages, 4 figures, 11 mathematical equations

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., Comment: 49 pages, 17 figures; v2: minor corrections

We present a simple closed form expression for the topologically twisted index of the ABJM theory as a function of the magnetic fluxes and complex chemical potentials valid at fixed $k$ and to all orders in the $1/N$ expansion. This in turn leads to analytic expressions for the topologically twisted index at fixed genus in the 't Hooft limit to all orders in the $1/\sqrt{\lambda}$ expansion. These results have important implications for holography and the microscopic entropy counting of supersymmetric static AdS$_4$ black holes. Generalizations to other SCFTs arising from M2-branes are also briefly discussed., Comment: 6 pages; v2: conjecture on the deformed 3-sphere partition function added, updated references; v3: minor typos corrected, version accepted for publication; v4: updated references

We present a prototype for Wilsonian analysis of asymptotics of supersymmetric partition functions of non-abelian gauge theories. Localization allows expressing such partition functions as an integral over a BPS moduli space. When the limit of interest introduces a scale hierarchy in the problem, asymptotics of the partition function is obtained in the Wilsonian approach by $i)$ decomposing (in some suitable scheme) the BPS moduli space into various patches according to the set of light fields (lighter than the scheme dependent cut-off $\Lambda$) they support, $ii)$ localizing the partition function of the effective field theory on each patch (with cut-offs set by the scheme), and $iii)$ summing up the contributions of all patches to obtain the final asymptotic result (which is scheme-independent and accurate as $\Lambda\to\infty$). Our prototype concerns the Cardy-like asymptotics of the 4d superconformal index, which has been of interest recently for its application to black hole microstate counting in AdS$_5$/CFT$_4$. As a byproduct of our analysis we obtain the most general asymptotic expression for the index of gauge theories in the Cardy-like limit, encompassing and extending all previous results., Comment: 56 pages, 2 figures. A short presentation of Section 2 is available at http://scgp.stonybrook.edu/video_portal/video.php?id=4953 v4: typos corrected

We investigate the large-$N$ asymptotics of the topologically twisted index of $\mathcal N=4$ SU($N$) Super-Yang-Mills (SYM) theory on $T^2\times S^2$ and provide its holographic interpretation based on the black hole Farey tail. In the field theory side, we use the Bethe-Ansatz (BA) formula, which gives the twisted index of $\mathcal N=4$ SYM theory as a discrete sum over Bethe vacua, to compute the large-$N$ asymptotics of the twisted index. In a dual $\mathcal N=2$ gauged STU model, we construct a family of 5d extremal solutions uplifted from the 3d black hole Farey tail, and compute the regularized on-shell actions. The gravitational partition function given in terms of these regularized on-shell actions is then compared with a canonical partition function derived from the twisted index by the inverse Laplace transform, in the large-$N$ limit. This extends the previous microstate counting of an AdS$_5$ black string by the twisted index and thereby improves holographic understanding of the twisted index., Comment: v1: 50 pages; v2: references added

We investigate the $S^3$ free energy of $\mathcal N=3$ Chern-Simons-matter quiver gauge theories with gauge group $U(N)^r~(r\geq2)$ where the sum of Chern-Simons levels does not vanish, beyond the leading order in the large-$N$ expansion. We take two different approaches to explore the sub-leading structures of the free energy. First we evaluate the matrix integral for the partition function in the 't~Hooft limit using a saddle point approximation. Second we use an ideal Fermi-gas model to compute the same partition function, but in the limit of fixed Chern-Simons levels. The resulting expressions for the free energy $F=-\log Z$ are consistent with each other at the leading and first sub-leading order. The Fermi-gas approach also hints at a universal $\frac{1}{6}\log N$ correction to the free energy. Since the quiver gauge theories we consider are dual to massive Type IIA theory, we expect our results to match sub-leading corrections to the holographic dual free energy, which have not yet been fully investigated., Comment: v1: 50 pages, 1figure; v2: minor revisions

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., Comment: v1: 36 pages, 4 figures; v2: corrected the conjecture in section 4.2, added a table in Appendix B; v3: minor revisions

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., Comment: 55 pages, 9 figures; v2: minor revisions; v3: minor revisions in p.14,20,23; v4: minor revisions in Appendix A; v5: correct minor typos in Appendix C

We study the Cardy-like asymptotics of the 4d $\mathcal N=4$ index and demonstrate the existence of partially deconfined phases where the asymptotic growth of the index is not as rapid as in the fully deconfined case. We then take the large-$N$ limit after the Cardy-like limit and make a conjecture for the leading asymptotics of the index. While the Cardy-like behavior is derived using the integral representation of the index, we demonstrate how the same results can be obtained using the Bethe ansatz type approach as well. In doing so, we discover new non-standard solutions to the elliptic Bethe ansatz equations including continuous families of solutions for $SU(N)$ theory with $N\ge3$. We argue that the existence of both standard and continuous non-standard solutions has a natural interpretation in terms of vacua of $\mathcal N=1^*$ theory on $\mathbb R^3\times S^1$., Comment: 54 pages, 8 figures; v2: minor revisions, references added; v3: minor revisions, footnote 2 and references added; v4: minor corrections in Appendix C

We construct necessary and sufficient geometric conditions for a class of AdS$_2$ solutions of M-theory with, at least, minimal supersymmetry to exist. We generalize previous results in the literature for ${\cal N}=(2,0)$ supersymmetry in AdS$_2$ to ${\cal N}=(1,0)$. When the solution can be locally described as AdS$_2\times \Sigma_g \times \,$SE$_7$ with $\Sigma_g$ a Riemann surface of genus $g$ and SE$_7$ a seven-dimensional Sasaki-Einstein manifold, we clarify and unify various solutions present in the literature. In the case of SE$_7=Q^{1,1,1}$ we find a new solution with baryonic and mesonic charges turned on simultaneously., Comment: 40 pages, 10 figures; v2: typos corrected, references added; v3: A summarizing table and references added, JHEP version

We study nearly extreme black holes with nearly AdS$_2$ horizon geometry in various settings inspired by string theory. Our focus is on the scales of the nAdS$_2$ region and their relation to microscopic theory. These scales are determined by a generalization of the attractor mechanism for extremal black holes and realized geometrically as the normal derivatives along the extremal attractor flow. In some cases the scales are equivalently determined by the charge dependence of the extremal attractor by itself. Our examples include near extreme black holes in $D\geq 4$ dimensions, AdS boundary conditions, rotation, and 5D black holes on the non-BPS branch., Comment: 42 pages; v2: minor revisions; v3: discussion section added

We find a family of complete non-linear Kaluza-Kein reduction ansatze from type IIB supergravity to Romans' 6D $F(4)$ gauged supergravity in the bosonic sector. The reduction is over a sphere $S^2$ and a Riemann surface $\Sigma$, and depends on a pair of arbitrary locally holomorphic functions $\mathcal{A}_{\pm}$ on $\Sigma$. This family of reductions is inspired by the recent construction of 1/2 BPS supersymmetric warped $AdS_6$ solutions of IIB supergravity that depend on these same functions $\mathcal{A}_{\pm}$., Comment: 16 pages; v2: added refs and minor revisions

The future power grid will be characterized by the pervasive use of heterogeneous and non-proprietary information and communication technology, which exposes the power grid to a broad scope of cyber-attacks. In particular, Monitoring-Control Attacks (MCA) --i.e., attacks in which adversaries manipulate control decisions by fabricating measurement signals in the feedback loop-- are highly threatening. This is because, MCAs are (i) more likely to happen with greater attack surface and lower cost, (ii) difficult to detect by hiding in measurement signals, and (iii) capable of inflicting severe consequences by coordinating attack resources. To defend against MCAs, we have developed a semantic analysis framework for Intrusion Detection Systems (IDS) in power grids. The framework consists of two parts running in parallel: a Correlation Index Generator (CIG), which indexes correlated MCAs, and a Correlation Knowledge-Base~(CKB), which is updated aperiodically with attacks' Correlation Indices (CI). The framework has the advantage of detecting MCAs and estimating attack consequences with promising runtime and detection accuracy. To evaluate the performance of the framework, we computed its false alarm rates under different attack scenarios., Comment: 10 pages, 8 figures

We examine the topologically twisted index of $\mathcal N=4$ super-Yang-Mills with gauge group $SU(N)$ on $T^2\times S^2$, and demonstrate that it receives contributions from multiple sectors corresponding to the freely acting orbifolds $T^2/\mathbb Z_m\times\mathbb Z_n$ where $N=mn$. After summing over these sectors, the index can be expressed as the elliptic genus of a two-dimensional $\mathcal N=(0,2)$ theory resulting from Kaluza-Klein reduction on $S^2$. This provides an alternate path to the 'high-temperature' limit of the index, and confirms the connection to the right-moving central charge of the $\mathcal N=(0,2)$ theory., Comment: 29 pages, 1 figure; v2: restricted to real chemical potentials in section 4 and added a comment on the index where $c_r(\mathfrak n_a)<0$ in section 5