Effective Gravitational Couplings of Higher-Rank Supersymmetric Gauge Theories

Abstract

When placed on four-manifolds, $\mathcal{N}=2$ gauge theories couple to topological invariants of the background via two functions $A$ and $B$. General considerations allow for these functions to be fixed in terms of the Coulomb moduli and other parameters in the theory, but only up to multiplicative factors about which little is known. We extend earlier work on the microscopic study of these functions in the $\Omega$-background to $\mathcal{N}=2^{\star }$ gauge theories with higher-rank $\mathrm{U}(N)$ gauge groups. We complement this analysis by carrying out a perturbative study of these functions. This allows us to determine the manner in which these multiplicative factors scale with the rank of the gauge group and the mass of the adjoint hypermultiplet.

arXiv comment22 pages

References in corpus (27)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
• Naturalness Versus Supersymmetric Non-renormalization Theorems
• D-particle bound states and generalized instantons
• Multi-Instanton Calculus and Equivariant Cohomology
• Positivity Constraints on Anomalies in Supersymmetric Gauge Theories
• Issues in Topological Gauge Theory
• Central charges of N=2 superconformal field theories in four dimensions
• Correlation Functions of Conserved Currents in N = 2 Superconformal Theory
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• BPS/CFT correspondence II: Instantons at crossroads, Moduli and Compactness Theorem
• BPS/CFT Correspondence III: Gauge Origami partition function and qq-characters
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• The Donaldson-Witten function for gauge groups of rank larger than one
• Non-perturbative gauge/gravity correspondence in N=2 theories
• Superconformal invariance and the geography of four-manifolds
• Modular anomaly equations in N=2* theories and their large-N limit
• Duality in twisted N=4 supersymmetric gauge theories in four dimensions
• Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories
• S-duality, triangle groups and modular anomalies in N=2 SQCD
• Elliptic Loci of SU(3) Vacua
• Chiral observables and S-duality in N = 2* U(N) gauge theories

Cited by in corpus (2)

• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Effective Gravitational Couplings of Kaluza-Klein Gauge Theories