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Register a new userA note on instanton operators, instanton particles, and supersymmetry
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We clarify certain aspects of instanton operators in five-dimensional supersymmetric gauge theories. In particular, we show how, in the pointlike limit, they become supersymmetric and provide the natural bridge with the instantonic states contributing to the index as well as with the zero mode counting leading to broken current multiplets.
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We present the calculation of the leading instanton contribution to the scaling dimensions of twist-two operators with arbitrary spin and to their structure constants in the OPE of two half-BPS operators in $mathcal N=4$ SYM. For spin-two operators we verify that, in agreement with $mathcal N=4$ superconformal Ward identities, the obtained expressions coincide with those for the Konishi operator. For operators with high spin we find that the leading instanton correction vanishes. This arises as the result of a rather involved calculation and requires a better understanding.
In the localization of 5-dimensional N = 1 super-Yang-Mills, contact-instantons arise as non-perturbative contributions. In this note, we revisit such configurations and discuss their generalizations. We propose for contact-instantons a cohomological theory whose BRST observables are invariants of the background contact geometry. To make the formalism more concrete, we study the moduli problem of contact- instanton, and we find that it is closely related to the eqiuivariant index of a canonical Dirac-Kohn operator associated to the geometry. An integral formula is given when the geometry is K-contact. We also discuss the relation to 5d N = 1 super-Yang- Mills, and by studying a contact-instanton solution canonical to the background geometry, we discuss a possible connection between N = 1 theory and contact homology. We also uplift the 5d theory a 6d cohomological theory which localizes to Donaldson-Uhlenbeck-Yau instantons when placed on special geometry.
We study SYM gauge theories living on ALE spaces. Using localization formulae we compute the prepotential (and its gravitational corrections) for SU(N) supersymmetric ${cal N}=2, 2^*$ gauge theories on ALE spaces of the $A_n$ type. Furthermore we derive the Poincar{e} polynomial describing the homologies of the corresponding moduli spaces of self-dual gauge connections. From these results we extract the ${cal N}=4$ partition function which is a modular form in agreement with the expectations of $SL(2,Z)$ duality.
A central object in any axionic theory is its periodic potential, which is typically generated by instantons. The goal of this paper is to understand what physically happens to the theory when we lose control of the potentials instanton expansion. We argue, using the Yang-Lee theory of phase transitions, that the theory breaks down in the classic sense: states become light. However, these states are not necessarily light for all values of the axion and there can be large regions where the effective description remains valid. We find alternative expressions for the effective potential in terms of the properties of these light states, which remain useful even when the instanton expansion breaks down, and thus initiate a push beyond the lamppost of large instanton actions. Most of these questions are motivated by the axionic Weak Gravity Conjecture, which we reformulate without reference to instanton actions. We also comment on its ability to constrain large-field axion inflation.
We present closed-form expressions of unrefined instanton partition functions for gauge groups of type $BCD$ as sums over Young diagrams. For $mathrm{SO}(n)$ gauge groups, we provide a fivebrane web picture of our formula based on the vertex-operator formalism of the topological vertex with a new type called O-vertex for an O5-plane.
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