Euclidean actions, instantons, solitons and supersymmetry

120

We present a new formulation of the local c-map, which makes use of a symplectically covariant real formulation of special Kähler geometry. We obtain an explicit and simple expression for the resulting quaternionic, or, in the case of reduction over time, para-quaternionic Kähler metric in terms of the Hesse potential, which is similar to the expressions for the metrics obtained from the rigid r-and c-map, and from the local r-map.As an application we use the temporal version of the c-map to derive the black hole attractor equations from geometric properties of the scalar manifold, without imposing supersymmetry or spherical symmetry. We observe that for general (non-symmetric) c-map spaces static BPS solutions are related to a canonical family of totally isotropic, totally geodesic submanifolds. Static non-BPS solutions can be obtained by applying a field rotation matrix which is subject to a non-trivial compatibility condition. We show that for a class of prepotentials, which includes the very special ('cubic') prepotentials as a subclass, axion-free solutions always admit a non-trivial field rotation matrix.

Section: Solitons and Instantonssupporting

confidence: 80%

The Hesse potential, the c-map and black hole solutions

Mohaupt

Vaughan

2012

120

“…In this sense, the name extremal instanton for flat 4d solutions (2.4) is justified. In section 4 we comment on how to express the extremal instanton action in terms of and M ADM , consistent with, for instance, [17,89,99].…”

Section: Jhep02(2017)097mentioning

confidence: 92%

“…This problem has been intensively investigated in the past, see e.g. [1,28,[76][77][78][79][80][81][82][83][84][85][86][87][88][89] and our present understanding mainly derives from [86][87][88]. Indeed, it should be possible to resolve the problem by dualising under the Euclidean path integral and following the fate of the instanton solution.…”

Section: Jhep02(2017)097mentioning

confidence: 99%

See 1 more Smart Citation

Can gravitational instantons really constrain axion inflation?

Hebecker¹,

Mangat²,

Theisen

et al. 2017

100

Axions play a central role in inflationary model building and other cosmological applications. This is mainly due to their flat potential, which is protected by a global shift symmetry. However, quantum gravity is known to break global symmetries, the crucial effect in the present context being gravitational instantons or Giddings-Strominger wormholes. We attempt to quantify, as model-independently as possible, how large a scalar potential is induced by this general quantum gravity effect. We pay particular attention to the crucial issue which solutions can or cannot be trusted in the presence of a moduli-stabilisation and a Kaluza-Klein scale. An important conclusion is that, due to specific numerical prefactors, the effect is surprisingly small even in UV-completions with the highest possible scale offered by string theory.As we go along, we discuss in detail Euclidean wormholes, cored and extremal instantons, and how the latter arise from 5d Reissner-Nordström black holes. We attempt to dispel possible doubts that wormholes contribute to the scalar potential by an explicit calculation. We analyse the role of stabilised dilaton-like moduli. Finally, we argue that Euclidean wormholes may be the objects satisfying the Weak Gravity Conjecture extended to instantons.

“…Lagrangian is complex-valued, and holomorphic, since it does not involve complex conjugation. As in [19] it does not seem to have a direct physical interpretation 13 but can be thought of as a 'holomorphic master Lagrangian,' 13 Except possibly in terms of a complexified configuration space which contains the complex saddle points of a Euclidean functional integral, see for example [26,27]. encoding all the possible real forms.…”

Section: Supersymmetric Lagrangiansmentioning

confidence: 99%

Five-dimensional vector multiplets in arbitrary signature

Gall

Mohaupt

2018

We start developing a formalism which allows to construct supersymmetric theories systematically across space-time signatures. Our construction uses a complex form of the supersymmetry algebra, which is obtained by doubling the spinor representation. This allows one to partially disentangle the Lorentz and R-symmetry group and generalizes symplectic Majorana spinors. For the case where the spinor representation is complex-irreducible, the R-symmetry only acts on an internal multiplicity space, and we show that the connected groups which occur are SO(2), SO 0 (1, 1), SU (2) and SU (1, 1).As an application we construct the off-shell supersymmetry transformations and supersymmetric Lagrangians for five-dimensional vector multiplets in arbitrary signature (t, s). In this case the R-symmetry groups are SU (2) or SU (1, 1), depending on whether the spinor representation carries a quaternionic or para-quaternionic structure. In Euclidean signature the scalar and vector kinetic terms differ by a relative sign, which is consistent with previous results in the literature and shows that this sign flip is an inevitable consequence of the Euclidean supersymmetry algebra.