Anomaly Matching Across Dimensions and Supersymmetric Cardy Formulae

Abstract

't Hooft anomalies are known to induce specific contributions to the effective action at finite temperature. We present a general method to directly calculate such contributions from the anomaly polynomial of a given theory, including a term which involves a $U(1)$ connection for the thermal circle isometry. Based on this observation, we show that the asymptotic behavior of the superconformal index of $4d$ $\mathcal{N}=1$ theories on the "second sheet" can be calculated by integrating the anomaly polynomial on a particular background. The integration is then performed by an equivariant method to reproduce known results. Our method only depends on the anomaly polynomial and therefore the result is applicable to theories without known Lagrangian formulation. We also present a new formula that relates the behavior of $6d$ $\mathcal{N}=(1,0)$ SCFTs on the second sheet to the anomaly polynomial.

arXiv comment34 pages; v2: minor edits, added references and comments

References in corpus (59)

• The Chiral Magnetic Effect
• Generalized Global Symmetries
• Hydrodynamics with Triangle Anomalies
• An Index for 4 dimensional Super Conformal Theories
• Counting chiral primaries in N=1 d=4 superconformal field theories
• Rigid Supersymmetric Theories in Curved Superspace
• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• Theta, Time Reversal, and Temperature
• Gravitational Anomaly and Transport
• Constraints on Fluid Dynamics from Equilibrium Partition Functions
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• The Omega Deformation, Branes, Integrability, and Liouville Theory
• Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
• Relativistic Hydrodynamics with General Anomalous Charges
• Thermodynamics, gravitational anomalies and cones
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Holographic Gravitational Anomaly and Chiral Vortical Effect
• M5-branes from gauge theories on the 5-sphere
• The Geometry of Supersymmetric Partition Functions
• Anomaly polynomial of general 6d SCFTs
• Supersymmetry on Curved Spaces and Holography
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Non-abelian Tensor-multiplet Anomalies
• Exploring Curved Superspace
• An extremization principle for the entropy of rotating BPS black holes in AdS${}_5$
• Black holes in 4d $\mathcal{N}=4$ Super-Yang-Mills
• (Non)-Renormalization of the Chiral Vortical Effect Coefficient
• Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories
• Localization and Diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories
• The asymptotic growth of states of the 4d N=1 superconformal index
• Anomaly/Transport in an Ideal Weyl gas
• Anomaly inflow and thermal equilibrium
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• A 4d N=1 Cardy Formula
• Triangle Anomalies, Thermodynamics, and Hydrodynamics
• Chern-Simons terms from thermal circles and anomalies
• Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS${}_5$ blackholes
• Anomaly polynomial of E-string theories
• 6d, N=(1,0) Coulomb Branch Anomaly Matching
• EFT and the SUSY Index on the 2nd Sheet
• Liouville/Toda central charges from M5-branes
• Asymptotic growth of the 4d $\mathcal{N}=4$ index and partially deconfined phases
• The supersymmetric index in four dimensions
• Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey
• Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
• High-Temperature Expansion of Supersymmetric Partition Functions
• Delayed Deconfinement and the Hawking-Page Transition
• Anomalies of QFTs from M-theory and Holography
• Anomalies, Black strings and the charged Cardy formula
• Cardy Formula for 4d SUSY Theories and Localization
• Supersymmetric Renyi Entropy and Anomalies in Six-Dimensional (1,0) Superconformal Theories
• AdS${}_7$ Black-Hole Entropy and 5D $\mathcal{N}=2$ Yang-Mills
• $C_T$ for higher derivative conformal fields and anomalies of (1,0) superconformal 6d theories
• An introduction to supersymmetric field theories in curved space
• Decomposition of BPS Moduli Spaces and Asymptotics of Supersymmetric Partition Functions
• $\mathcal{N}=(1,0)$ Anomaly Multiplet Relations in Six Dimensions

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