Euclidean Actions, Instantons, Solitons and Supersymmetry

Abstract

Theories with axionic scalars admit three different Euclidean formulations, obtained by Wick rotation, Wick rotation combined with analytic continuation of the axionic scalars, and Wick rotation combined with Hodge dualization. We investigate the relation between these formulations for a class of theories which contains the sigma models of N=2 vector multiplets as a special case. It is shown that semi-classical amplitudes can be expressed equivalently using the two types of axionic actions, while the Hodge dualized version gives a different value for the instanton action unless the integration constants associated with the axion fields are chosen in a particular way. With this choice the instanton action is equal to the mass of the soliton or black hole obtained by dimensional lifting with respect to time. For supersymmetric models we use the Euclidean supersymmetry algebra to derive a Euclidean BPS condition, and we identify a geometrical criterion which distinguishes BPS from non-BPS extremal solutions.

38 pages

References in corpus (34)

• A Geometry for Non-Geometric String Backgrounds
• Effects of D-instantons
• Timelike T-Duality, de Sitter Space, Large $N$ Gauge Theories and Topological Field Theory
• Direct, Indirect and Collider Detection of Neutralino Dark Matter In SUSY Models with Non-universal Higgs Masses
• Instantons and seven-branes in type IIB superstring theory
• Flow Equations for Non-BPS Extremal Black Holes
• On Euclidean spinors and Wick rotations
• First-order flow equations for extremal black holes in very special geometry
• M-theory from its superalgebra
• Special Geometry of Euclidean Supersymmetry I: Vector Multiplets
• Euclidean SYM Theories by Time Reduction and Special Holonomy Manifolds
• BPS Branes in Supergravity
• Metastable Vacua in Flux Compactifications and Their Phenomenology
• Quantum Attractor Flows
• Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes
• Metrics Admitting Killing Spinors In Five Dimensions
• Pseudo-supersymmetry and a Tale of Alternate Realities
• Supergravity Instantons for N=2 Hypermultiplets
• Instantons in the Double-Tensor Multiplet
• Supergravity Instantons and the Universal Hypermultiplet
• Non-extremal Black Holes, Harmonic Functions, and Attractor Equations
• From Type IIA Black Holes to T-dual Type IIB D-Instantons in N=2, D=4 Supergravity
• $Q\bar{Q}$ potential from AdS-CFT relation at $T\ge 0$: Dependence on orientation in internal space and higher curvature corrections
• N=2 Supergravity Lagrangians with Vector-Tensor Multiplets
• Instantons, black holes and harmonic functions
• Instantons, Euclidean supersymmetry and Wick rotations
• Instanton Solutions for the Universal Hypermultiplet
• Supergravity description of spacetime instantons
• A continuous Wick rotation for spinor fields and supersymmetry in Euclidean space
• Ward Identities for N=2 Rigid and Local Supersymmetry in Euclidean Space
• Instantons and Wormholes in N=2 supergravity
• The low-energy effective action for perturbative heterotic strings on $K_3\times T^2$ and the d=4 N=2 vector-tensor multiplet
• Recent results in four-dimensional non-perturbative string theory
• Geometric construction of the r-map: from affine special real to special Kähler manifolds

Cited by in corpus (6)

• Euclidean wormholes, baby universes, and their impact on particle physics and cosmology
• Special Geometry, Hessian Structures and Applications
• Five-dimensional vector multiplets in arbitrary signature
• Non-extremal black hole solutions from the c-map
• Developments in special geometry
• Type-II Calabi-Yau compactifications, T-duality and special geometry in general spacetime signature