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Register a new userAnomalies, D-flatness and Small Instantons
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Authors
R.G. Leigh
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Recently, Witten has proposed a mechanism for symmetry enhancement in $SO(32)$ heterotic string theory, where the singularity obtained by shrinking an instanton to zero size is resolved by the appearance of an $Sp(1)$ gauge symmetry. In this short letter, we consider spacetime constraints from anomaly cancellation in six dimensions and D-flatness and demonstrate a subtlety which arises in the moduli space when many instantons are shrunk to zero size.
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All five-dimensional non-abelian gauge theories have a $U(1)_I$ global symmetry associated with instantonic particles. We describe an obstruction to coupling $U(1)_I$ to a classical background gauge field that occurs whenever the theory has a one-form center symmetry. This is a finite-order mixed t Hooft anomaly between the two symmetries. We also show that a similar obstruction takes place in gauge theories with fundamental matter by studying twisted bundles for the ordinary flavor symmetry. We explore some general dynamical properties of the candidate phases implied by the anomaly. Finally, we apply our results to supersymmetric gauge theories in five dimensions and analyze the symmetry enhancement patterns occurring at their conjectured RG fixed points.
We construct the most general non-extremal deformation of the D-instanton solution with maximal rotational symmetry. The general non-supersymmetric solution carries electric charges of the SL(2,R) symmetry, which correspond to each of the three conjugacy classes of SL(2,R). Our calculations naturally generalise to arbitrary dimensions and arbitrary dilaton couplings. We show that for specific values of the dilaton coupling parameter, the non-extremal instanton solutions can be viewed as wormholes of non-extremal Reissner-Nordstrom black holes in one higher dimension. We extend this result by showing that for other values of the dilaton coupling parameter, the non-extremal instanton solutions can be uplifted to non-extremal non-dilatonic p-branes in p+1 dimensions higher. Finally, we attempt to consider the solutions as instantons of (compactified) type IIB superstring theory. In particular, we derive an elegant formula for the instanton action. We conjecture that the non-extremal D-instantons can contribute to the R^8-terms in the type IIB string effective action.
We point out that in some situations it is possible to use matrix model techniques a la Dijkgraaf-Vafa to perturbatively compute D-brane instanton effects. This provides an explanation in terms of stringy instantons of the results in hep-th/0311181. We check this proposal in some simple scenarios. We point out some interesting consequences of this observation, such as the fact that it gives a perturbative way of computing stringy multi-instanton effects. It also provides a further interpretation of D-brane instantons as residual instantons of higgsed supergroups.
Instanton is known to exist in Euclidean spacetime only. Their role in real time dynamics is usually understood as tunneling effect by Wick rotation. We illustrate other effects of instanton in holography by investigating 5d effective gravity theory of the black D3-brane-D-instanton system. The supergravity description of the D3-brane-D-instanton system is dual to the super Yang-Mills theory with topological excitations of the vacuum. We obtain Euclidean correlators in the presence of instantons by analyzing of the fluctuations of the bulk fields in the 5d effective theory. Furthermore, analytic continuation of Euclidean correlators leads to retarded correlators, which characterize real time dynamics. We find interestingly real time fluctuations of topological charge can destroy instantons and the lifetime of instanton is set by temperature. This implies instanton contribution to real time dynamics is suppressed at high temperature, which is analogous to classic field theory results that instanton contribution to thermodynamics is suppressed at high temperature.
We investigate non-extremal D-instantons in an asymptotically $ AdS_5 times S^5$ background and the role they play in the $ AdS_5 / CFT_4$ correspondence. We find that the holographic dual operators of non-extremal D-instanton configurations do not correspond to self-dual Yang-Mills instantons, and we compute explicitly the deviation from self-duality. Furthermore, a class of non-extremal D-instantons yield Euclidean axionic wormhole solutions with two asymptotic boundaries. After Wick rotating, this provides a playground for investigating holography in the presence of cosmological singularities in a closed universe.
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