SYM on quotients of spheres and complex projective spaces

Lundin, Jim; Ruggeri, Lorenzo

doi:10.1007/jhep03(2022)204

Cited by 5 publications

(6 citation statements)

References 39 publications

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“…We further require that i a i = 0. 2r−1 can be seen as a fibration over r−1 and this condition ensures that the squashing acts only on the base r−1 [22]. For a physical squashed sphere ω i ∈ + , but it will be necessary to give them a small imaginary piece in order to have a well behaved partition function.…”

Section: Preliminariesmentioning

confidence: 99%

Seven-dimensional super Yang-Mills at negative coupling

2023

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We consider the partition function for Euclidean SU(N)SU(N) super Yang-Mills on a squashed seven-sphere. We show that the localization locus of the partition function has instanton membrane solutions wrapping the six ``fixed" three-spheres on the \mathbb{S}^7𝕊7. The ADHM variables of these instantons are fields living on the membrane world volume. We compute their contribution by localizing the resulting three-dimensional supersymmetric field theory. In the round-sphere limit the individual instanton contributions are singular, but the singularities cancel when adding the contributions of all six three-spheres. The full partition function on the {\mathbb S}^7𝕊7 is well-defined even when the square of the effective Yang-Mills coupling is negative. We show for an SU(2)SU(2) gauge theory in this regime that the bare negative tension of the instanton membranes is canceled off by contributions from the instanton partition function, indicating the existence of tensionless membranes. We provide evidence that this phase is distinct from the usual weakly coupled super Yang-Mills and, in fact, is gravitational.

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Section: Preliminariesmentioning

confidence: 99%

Seven-dimensional super Yang-Mills at negative coupling

2023

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“…This example has been discussed in detail in [37] and we include it here for completeness. The metric cone is C(S 5 ) = C 3 .…”

Section: Smentioning

confidence: 99%

“…The setup above is related to the study of two-dimensional weighted projective spaces, also known as spindles [61]. In [37] the reduction of an N = 2 vector multiplet from S 3 to S 2 is considered. As a consistency check, taking an N = 1 vector multiplet S 3 × S 1 as starting point and generalizing the reduction to locally free S 1 -actions, one should reproduce the result of [62] for both topological and exotic theories.…”

Section: Jhep10(2023)155mentioning

confidence: 99%

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From 5d flat connections to 4d fluxes (the art of slicing the cone)

Lundin,

Mauch,

Ruggeri

2023

J. High Energ. Phys.

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We compute the Coulomb branch partition function of the 4d $$ \mathcal{N} $$ N = 2 vector multiplet on closed simply-connected quasi-toric manifolds B. This includes a large class of theories, localising to either instantons or anti-instantons at the torus fixed points (including Donaldson-Witten and Pestun-like theories as examples). The main difficulty is to obtain flux contributions from the localisation procedure. We achieve this by taking a detour via the 5d $$ \mathcal{N} $$ N = 1 vector multiplet on closed simply-connected toric Sasaki-manifolds M which are principal S1-bundles over B. The perturbative partition function can be expressed as a product over slices of the toric cone. By taking finite quotients M/ℤh along the S1, the locus picks up non-trivial flat connections which, in the limit h → ∞, provide the sought-after fluxes on B. We compute the one-loop partition functions around each topological sector on M/ℤh and B explicitly, and then factorise them into contributions from the torus fixed points. This enables us to also write down the conjectured instanton part of the partition function on B.

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“…We further require that i a i = 0. S 2r−1 can be seen as a fibration over CP r−1 and this condition ensures that the squashing acts only on the base CP r−1 [22]. For a physical squashed sphere ω i ∈ R + , but it will be necessary to give them a small imaginary piece in order to have a well behaved partition function.…”

Section: Preliminariesmentioning

confidence: 99%

Seven-dimensional super Yang-Mills at negative coupling

Minahan¹,

Naseer²,

Thull³

2022

Preprint

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We consider the partition function for Euclidean SU (N ) super Yang-Mills on a squashed seven-sphere. We show that the localization locus of the partition function has instanton membrane solutions wrapping the six "fixed" three-spheres on the S 7 . The ADHM variables of these instantons are fields living on the membrane world volume. We compute their contribution by localizing the resulting three-dimensional supersymmetric field theory. In the round-sphere limit the individual instanton contributions are singular, but the singularities cancel when adding the contributions of all six three-spheres.The full partition function on the S 7 is well-defined even when the square of the effective Yang-Mills coupling is negative. We show for an SU (2) gauge theory in this regime that the bare negative tension of the instanton membranes is canceled off by contributions from the instanton partition function, indicating the existence of tensionless membranes. We provide evidence that this phase is distinct from the usual weakly coupled super Yang-Mills and, in fact, is gravitational.

show abstract

SYM on quotients of spheres and complex projective spaces

Cited by 5 publications

References 39 publications

Seven-dimensional super Yang-Mills at negative coupling

Seven-dimensional super Yang-Mills at negative coupling

From 5d flat connections to 4d fluxes (the art of slicing the cone)

Seven-dimensional super Yang-Mills at negative coupling

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