arXiv subjects

Johannes Schmude

Publications and source records attributed to Johannes Schmude.

29 records · Page 2Linked to original sources

arXiv2014

Partition functions for equivariantly twisted $\mathcal{N}=2$ gauge theories on toric Kähler manifolds

We consider $\mathcal{N}=2$ supersymmetric pure gauge theories on toric Kähler manifolds, with particular emphasis on $\mathbb{CP}^2$. By choosing a vector generating a $U(1)$ action inside the torus of the manifold, we construct equivariantly twisted theories. Then, using localization, we compute their supersymmetric partition functions. As expected, these receive contributions from a classical, a one-loop, and an instanton term. It turns out that the one-loop term is trivial and that the instanton contributions are localized at the fixed points of the $U(1)$. In fact the full partition function can be re-written in a factorized form with contributions from each of the fixed points. The full significance of this is yet to be understood.

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arXiv2014

Localisation on Sasaki-Einstein manifolds from holomophic functions on the cone

We study super Yang-Mills theories on five-dimensional Sasaki-Einstein manifolds. Using localisation techniques, we find that the contribution from the vector multiplet to the perturbative partition function can be calculated by counting holomorphic functions on the associated Calabi-Yau cone. This observation allows us to use standard techniques developed in the context of quiver gauge theories to obtain explicit results for a number of examples; namely $S^5$, $T^{1,1}$, $Y^{7,3}$, $Y^{2,1}$, $Y^{2,0}$, and $Y^{4,0}$. We find complete agreement with previous results obtained by Qiu and Zabzine using equivariant indices except for the orbifold limits $Y^{p,0}$ with $p > 1$.

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arXiv2013

Laplace operators on Sasaki-Einstein manifolds

We decompose the de Rham Laplacian on Sasaki-Einstein manifolds as a sum over mostly positive definite terms. An immediate consequence are lower bounds on its spectrum. These bounds constitute a supergravity equivalent of the unitarity bounds in dual superconformal field theories. The proof uses a generalization of Kahler identities to the Sasaki-Einstein case.

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arXiv2013

Superconformal Indices, Sasaki-Einstein Manifolds, and Cyclic Homologies

The superconformal index of the quiver gauge theory dual to type IIB string theory on the product of an arbitrary smooth Sasaki-Einstein manifold with five-dimensional AdS space is calculated both from the gauge theory and gravity viewpoints. We find complete agreement. Along the way, we find that the index on the gravity side can be expressed in terms of the Kohn-Rossi cohomology of the Sasaki-Einstein manifold and that the index of a quiver gauge theory equals the Euler characteristic of the cyclic homology of the Ginzburg dg algebra associated to the quiver.

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arXiv2013

Superconformal Indices and M2-Branes

We derive the superconformal index of the world-volume theory on M2-branes probing the cone over an arbitrary Sasaki-Einstein seven-manifold. The index is expressed in terms of the cohomology groups of the cone. We match our supergravity results with known results from gauge theory. Along the way we derive the spectrum of short Kaluza-Klein multiplets on generic Sasaki-Einstein seven-manifolds.

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arXiv2012

On supersymmetry breaking three-form flux on Sasaki-Einstein manifolds

Studying nonsupersymmetric yet imaginary self-dual three-form fluxes in type IIB supergravity backgrounds on Sasaki-Einstein manifolds we find a new analytic solution that restores supersymmetry in the IR, breaks it at higher energies, yet suffers from curvature singularities in the UV, when a certain SUSY-breaking parameter becomes large. Consequently we investigate a variety of possibilities to cure the singularity by either introducing additional sources, changing the fluxes or deforming the geometry. Since it is not possible to cure the singularities making physically reasonably assumptions, we suggest that there might be a no-go theorem disallowing such flux.

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arXiv2010

Comments on the distinction between color- and flavor-branes and new D3-D7 solutions with eight supercharges

We investigate the distinction between color- and flavor-branes, that is usually made in the context of gauge/string duality with backreacting flavors. Our remarks are based on a series of examples concerning the role of source terms in relatively simple supergravity backgrounds that allow for a well-controlled approach to the problem. The observations suggest that, in opposite to general practice, one could consider such terms for both kinds of branes, while their presence is only essential for smeared sources - as is commonly the case for flavor-branes. Among the examples studied are D3-D7 systems with eight supercharges, where the D7-branes are assumed to be smeared. Starting from a fairly generic ansatz, we will find new analytic and numeric solutions and briefly compare these to previous work in this field.

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arXiv2010

The lift of type IIA supergravity with D6 sources: M-theory with torsion

This paper is concerned with an extension of the well known Kaluza-Klein mechanism. As the standard ansatz for Kaluza-Klein reduction implies the existence of a gauge potential associated with the KK field strength, it follows immediately that this field strength satisfies its Bianchi identity. Hence, the standard KK formalism breaks down in the presence of a violated Bianchi identity. This occurs for example in the context of D6 sources. We will investigate and partially solve this problem in the context of the type IIA/M-theory duality. Our discussion is motivated by the construction of gauge/string duals with backreacting flavor branes using D6-branes, which appear in M-theory as KK-monopoles. We are able to derive source-modified equations of motion for the eleven-dimensional theory, and are subsequently able to obtain the source-modified type IIA equations by direct dimensional reduction.

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arXiv2009

A note on backreacting flavors from calibrated geometry

One of the main problems in the search for string duals with backreacting, smeared flavors is the construction of a suitable source density. We review how this issue may be addressed using generalized calibrated geometry.

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arXiv2009

On the geometry of string duals with backreacting flavors

Making use of generalized calibrated geometry and G-structures we put the problem of finding string-duals with smeared backreacting flavor branes in a more mathematical setting. This more formal treatment of the problem allows us to easily smear branes without good coordinate representations, establish constraints on the smearing form and identify a topological central charge in the SUSY algebra. After exhibiting our methods for a series of well known examples, we apply them to the problem of flavoring a supergravity-dual to a d=2+1 dimensional N=2 super Yang-Mills-like theory. We find new solutions to both the flavored and unflavored systems. Interpretating these turns out to be difficult.

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arXiv2008

The quark-gluon plasma and D6-branes on the conifold

We investigate the possibility of constructing a supergravity background dual to the quark-gluon plasma using D6-branes wrapping a three-cycle in the deformed conifold. The UV-completion of this setup is given by M-theory on a G2 holonomy manifold. For the class of metrics considered we find that there are only non-extremal D-brane solutions in the limit of the singular conifold with the singularity being resolved by the D-brane horizon. The thermodynamic properties of the system show some puzzling features, such as negative specific heat at an unusual behavior of the entropy. Among the properties of the plasma studied using this holographic dual are the quark-antiquark potential, the shear viscosity and parton energy loss. While one finds the expected behavior for the potential and the viscosity -- deconfinement and the universal shear-viscosity to entropy ratio -- both the jet quenching parameter and the calculation of the drag force lead us to the conclusion that there is no parton energy loss in the dual plasma. Our results indicate that the background constructed is not dual to a realistic QGP, yet we argue that this should improve upon inclusion of the three-form gauge potential in the eleven-dimensional background.

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