The equivalence of Sp(2N) and SO(−2N) gauge theories

Mkrtchyan, R. L.

doi:10.1016/0370-2693(81)91015-7

Cited by 59 publications

(46 citation statements)

References 2 publications

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“…(3.7), so it is manifest that they differ just by a sign; this, together with the equality of the even terms in the expansions, proves that indeed W (g) Sp(N ) can be obtained from W (g) SO(2N ) by the substitution N → −N , as it had to happen according to general arguments [45,46].…”

Section: Jhep09(2014)169mentioning

confidence: 94%

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Exact probes of orientifolds

Fiol

Garolera

Torrents

2014

J. High Energ. Phys.

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We compute the exact vacuum expectation value of circular Wilson loops for Euclidean N = 4 super Yang-Mills with G = SO(N ), Sp(N ), in the fundamental and spinor representations. These field theories are dual to type IIB string theory compactified on AdS 5 × RP 5 plus certain choices of discrete torsion, and we use our results to probe this holographic duality. We first revisit the LLM-type geometries having AdS 5 × RP 5 as ground state. Our results clarify and refine the identification of these LLM-type geometries as bubbling geometries arising from fermions on a half harmonic oscillator. We furthermore identify the presence of discrete torsion with the one-fermion Wigner distribution becoming negative at the origin of phase space. We then turn to the string world-sheet interpretation of our results and argue that for the quantities considered they imply two features: first, the contribution coming from world-sheets with a single crosscap is closely related to the contribution coming from orientable world-sheets, and second, world-sheets with two crosscaps don't contribute to these quantities.

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Section: Jhep09(2014)169mentioning

confidence: 94%

“…Furthermore, gauge invariant quantities for Sp(N ) are related to those of SO(2N ) by the replacement N → −N [45,46]. Finally, we know that SO(2N ) and Sp(N ) theories can be obtained from orientifolding U (2N ).…”

Section: Jhep09(2014)169mentioning

confidence: 99%

Exact probes of orientifolds

Fiol

Garolera

Torrents

2014

J. High Energ. Phys.

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“…This generalizes the old N → −N duality of gauge theories with orthogonal and symplectic groups [15], and leads in particular to a suggestion of an extension of gauge/string duality to exceptional groups [16]. Furthermore, the integral representation is very well suited to study non-perturbative aspects of the large N duality, see [12,16].…”

Section: Jhep10(2015)045mentioning

confidence: 99%

Exact Chern-Simons / Topological String duality

Krefl

Mkrtchyan

2015

J. High Energ. Phys.

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Abstract:We invoke universal Chern-Simons theory to analytically calculate the exact free energy of the refined topological string on the resolved conifold. In the unrefined limit we reproduce non-perturbative corrections for the resolved conifold found elsewhere in the literature, thereby providing strong evidence that the Chern-Simons / topological string duality is exact, and in particular holds at arbitrary N . In the refined case, the non-perturbative corrections we find are novel and appear to be non-trivial. We show that non-perturbatively special treatment is needed for rational valued deformation parameter. Above results are also extended to refined Chern-Simons with orthogonal groups.

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“…Here is a meeting point with the recent studies of "universal formulas" in Lie algebra theory by Mkrtchyan and Veselov (see, in particular, [13], [11], [14], [12]). (One source of these ideas is [10], another is the works of Vogel and Deligne.) There remain many open questions here.…”

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confidence: 99%

Volumes of Classical Supermanifolds

Voronov¹

2018

Trends in Mathematics

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Abstract. We consider the volumes of classical supermanifolds such as the supersphere, complex projective superspace, and Stiefel and Grassmann supermanifolds, with respect to the natural metrics or symplectic structures. We show that the formulas for the volumes, upon certain universal normalization, can be obtained by an analytic continuation from the formulas for the volumes of the corresponding ordinary manifolds.Volumes of nontrivial supermanifolds may identically vanish. In 1970s, Berezin discovered that the total Haar measure of the unitary supergroup U(n|m) vanishes unless m = 0 or n = 0, i.e., unless it reduces to the ordinary unitary group U(n) or U(m). Witten recently suggested that the (Liouville) volume of a compact even symplectic supermanifold should always be zero if it is not an ordinary manifold. Our calculations provide counterexamples to this conjecture. On the other hand, we give a simple explanation of Berezin's statement and generalize it to the Stiefel supermanifold V r|s (C n|m ). There are also possible connections with the recent works by Mkrtchyan and Veselov on 'universal formulas' in Lie algebra theory.

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The equivalence of Sp(2N) and SO(−2N) gauge theories

Cited by 59 publications

References 2 publications

Exact probes of orientifolds

Exact probes of orientifolds

Exact Chern-Simons / Topological String duality

Volumes of Classical Supermanifolds

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