Five-dimensional gauge theories on spheres with negative couplings

Minahan, Joseph A.; Nedelin, Anton

doi:10.1007/jhep02(2021)102

Cited by 4 publications

(4 citation statements)

References 33 publications

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“…where λ is the dimensionless 't Hooft coupling λ = g 2 YM N R −3 . These equations are very similar to those found for pure N = 1 super Yang-Mills on S 5 [25] so we can borrow many of the methods from there. We are most interested in having λ be small and negative.…”

Section: The Round Spheresupporting

confidence: 62%

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.

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Section: The Round Spheresupporting

confidence: 62%

Seven-dimensional super Yang-Mills at negative coupling

Minahan¹,

Naseer²,

Thull³

2022

Preprint

Self Cite

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“…Nevertheless, the perturbative partition function can be analytically continued letting h ∈ R in (2.3) but keeping the non-perturbative quantities, such as instanton masses, as functions of |h|. For a thorough discussion on negative Yang-Mills coupling, see [44,29]. Besides, the SPE (2.22) may be likewise analytically continued to negative values of the Veneziano parameters ζ α .…”

Section: Remarks On the Decompactification Limitmentioning

confidence: 99%

“…There exists a vast literature discussing the large N behaviour of 5d N = 1 theories on the sphere [18][19][20][21][22][23][24][25][26][27], mostly pivoting around the match with the holographic dual. A thorough analysis of the large N phases of certain theories on the five-sphere appears in the work of Minahan and Nedelin [28,29].…”

Section: Introductionmentioning

confidence: 99%

Phases of five-dimensional supersymmetric gauge theories

Santilli

2021

Preprint

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Five-dimensional N = 1 theories with gauge group U (N ), SU (N ), U Sp(2N ) and SO(N ) are studied at large rank through localization on a large sphere. The phase diagram of theories with fundamental hypermultiplets is universal and characterized by third order phase transitions, with the exception of U (N ), that shows both second and third order transitions. The phase diagram of theories with adjoint or (anti-)symmetric hypermultiplets is also determined and found to be universal. Moreover, Wilson loops in fundamental and antisymmetric representations of any rank are analyzed in this limit. Quiver theories are discussed as well. All the results substantiate the F-theorem.

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“…As in the five-dimensional case, the term linear in δσ i can be dropped for small negative λ. Moreover, in the large N limit δ 0 is suppressed by a factor of 1/N [25]. The remaining terms on the left hand side of (2.21) can be generated by the free energy…”

Section: The Round Spherementioning

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.

show abstract

Five-dimensional gauge theories on spheres with negative couplings

Cited by 4 publications

References 33 publications

Seven-dimensional super Yang-Mills at negative coupling

Seven-dimensional super Yang-Mills at negative coupling

Phases of five-dimensional supersymmetric gauge theories

Seven-dimensional super Yang-Mills at negative coupling

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