Instantons and Killing spinors

201

416

We use the 5-sphere partition functions of supersymmetric Yang-Mills theories to explore the (2, 0) superconformal theory on S 5 × S 1 . The 5d theories can be regarded as Scherk-Schwarz reductions of the 6d theory along the circle. In a special limit, the perturbative partition function takes the form of the Chern-Simons partition function on S 3 . With a simple non-perturbative completion, it becomes a 6d index which captures the degeneracy of a sector of BPS states as well as the index version of the vacuum Casimir energy. The Casimir energy exhibits the N 3 scaling at large N . The large N index for U (N ) gauge group also completely agrees with the supergravity index on AdS 7 × S 4 .

Section: Perturbative Partition Function and Casimir Energiesmentioning

confidence: 99%

M5-branes from gauge theories on the 5-sphere

Kim

2013

201

416

“…Higher-dimensional instanton equations generalise the self-dual YangMills equations in four dimensions, and were first constructed in [62][63][64]. The instanton condition can be reformulated as a G 2 invariant constraint [36,37,[65][66][67][68][69][70][71][72][73], and explicit solutions to the instanton condition on certain G 2 manifolds are also known [74,75]. Here, we show that the G 2 instanton condition is implied by a supersymmetry constraint in string compactifications, and that it, in turn, implies the Yang-Mills equations as an equation of motion of the theory.…”

Section: Jhep11(2016)016mentioning

confidence: 99%

“…The connection A on V is an instanton if for some real number ν (typically ν = ±1), the curvature F = dA + A ∧ A satisfies (see e.g. [68])…”

Section: Instantons and Yang-mills Equationsmentioning

confidence: 99%

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

Ossa

Larfors

Svanes

2016

Abstract:We describe the infinitesimal moduli space of pairs (Y, V ) where Y is a manifold with G 2 holonomy, and V is a vector bundle on Y with an instanton connection. These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g. domain walls. Employing the canonical G 2 cohomology developed by Reyes-Carrión and Fernández and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli H 1 d A (Y, End(V )) plus the moduli of the G 2 structure preserving the instanton condition. The latter piece is contained in H 1 d θ (Y, T Y ), and is given by the kernel of a mapF which generalises the concept of the Atiyah map for holomorphic bundles on complex manifolds to the case at hand. In fact, the mapF is given in terms of the curvature of the bundle and maps, and moreover can be used to define a cohomology on an extension bundle of T Y by End(V ). We comment further on the resemblance with the holomorphic Atiyah algebroid and connect the story to physics, in particular to heterotic compactifications on (Y, V ) when α = 0.

“…One may consider the situation when dη ∈ Ω 2 ± (M ) while F ∈ Ω 2 ∓ (M, End E M ) in which case dη ∧ F = 0. This is the situation that was considered by Harland & Nölle in the Sasaki-Einstein setting and for SU(2) as gauge group [10]. Therefore, we may conclude that the contact instanton equation with dη ∈ Ω 2 ± (M ) and F ∈ Ω 2 ± (M, End E M ) appears to be integrable via the above construction but does not automatically imply the [21] for the case of Spin(7)-instantons): in terms of our present setting of contact instantons on K-contact manifolds M with gauge group SU(r), the action functional is…”

Section: Remark 43mentioning

confidence: 86%

“…Proof: Using the frame fields {E αα , ξ}, the totally trace-free part of R − − is given by 10) where the parentheses indicate total normalised symmetrisation of all the enclosed dotted indices. Furthermore, in the case of conformal K-contact manifolds, the Gauß equation…”

Section: Twistor Construction Of Contact Manifoldsmentioning

confidence: 99%

Contact manifolds, contact instantons, and twistor geometry

Wolf

2012

Recently, Källén & Zabzine computed the partition function of a twisted supersymmetric Yang-Mills theory on the five-dimensional sphere using localisation techniques. Key to their construction is a five-dimensional generalisation of the instanton equation to which they refer as the contact instanton equation.Subject of this article is the twistor construction of this equation when formulated on K-contact manifolds and the discussion of its integrability properties.We also present certain extensions to higher dimensions and supersymmetric generalisations.