Anton Nedelin

Bio: Anton Nedelin is an academic researcher from Technion – Israel Institute of Technology. The author has contributed to research in topics: Gauge theory & Yang–Mills theory. The author has an hindex of 17, co-authored 29 publications receiving 891 citations. Previous affiliations of Anton Nedelin include University of Milan & University of Milano-Bicocca.

N 3-behavior from 5D Yang-Mills theory

Abstract: In this note we derive N 3-behavior at large ’t Hooft coupling for the free energy of 5D maximally supersymmetric Yang-Mills theory on S 5. We also consider a Z k quiver of this model, as well as a model with M hypermultiplets in the fundamental representation. We compare the results to the supergravity description and comment on their relation.

5D super Yang–Mills theory and the correspondence to AdS7/CFT6

Abstract: We study the relation between 5D super Yang–Mills theory and the holographic description of 6D (2, 0) superconformal theory. We start by clarifying some issues related to the localization of SYM with matter on S5. We concentrate on the case of a single adjoint hypermultiplet with a mass term and argue that the theory has a symmetry enlargement at mass M = 1/(2r), where r is the S5 radius. However, in order to have a well-defined localization locus it is necessary to rotate M onto the imaginary axis, breaking the enlarged symmetry. Based on our prescription, the imaginary mass values are physical and we show how the localized path integral is consistent with earlier results for 5D SYM in flat space. We then compute the free energy and the expectation value for a circular Wilson loop in the large N limit. The Wilson loop calculation shows a mass dependent constant rescaling between weak and strong coupling. The Wilson loop continued back to to the enlarged symmetry point is consistent with a supergravity computation for an M2 brane using the standard identification of the compactification radius and the 5D coupling. If we continue back to the physical regime and use this value of the mass to determine the compactification radius, then we find agreement between the SYM free energy and the corresponding supergravity calculation. We also verify numerically some of our analytic approximations.

The Cardy limit of the topologically twisted index and black strings in AdS5

Abstract: We evaluate the topologically twisted index of a general four-dimensional $$ \mathcal{N}=1 $$ gauge theory in the “high-temperature” limit. The index is the partition function for $$ \mathcal{N}=1 $$ theories on S 2 × T 2, with a partial topological twist along S 2, in the presence of background magnetic fluxes and fugacities for the global symmetries. We show that the logarithm of the index is proportional to the conformal anomaly coefficient of the two-dimensional $$ \mathcal{N}=\left(0,2\right) $$ SCFTs obtained from the compactification on S 2. We also present a universal formula for extracting the index from the four-dimensional conformal anomaly coefficient and its derivatives. We give examples based on theories whose holographic duals are black strings in type IIB backgrounds AdS5 × SE5, where SE5 are five-dimensional Sasaki-Einstein spaces.

The Cardy limit of the topologically twisted index and black strings in AdS$_5$

Abstract: We evaluate the topologically twisted index of a general four-dimensional $\mathcal{N} = 1$ gauge theory in the "high-temperature" limit. The index is the partition function for $\mathcal{N} = 1$ theories on $S^2 \times T^2$, with a partial topological twist along $S^2$, in the presence of background magnetic fluxes and fugacities for the global symmetries. We show that the logarithm of the index is proportional to the conformal anomaly coefficient of the two-dimensional $\mathcal{N} = (0,2)$ SCFTs obtained from the compactification on $S^2$. We also present a universal formula for extracting the index from the four-dimensional conformal anomaly coefficient and its derivatives. We give examples based on theories whose holographic duals are black strings in type IIB backgrounds AdS$_5 \times \text{SE}_5$, where SE$_5$ are five-dimensional Sasaki-Einstein spaces.

5D super Yang-Mills theory and the correspondence to AdS$_7$/CFT$_6$

Abstract: We study the relation between 5D super Yang-Mills theory and the holographic description of 6D (2,0) superconformal theory. We start by clarifying some issues related to the localization of N=1 SYM with matter on $S^5$. We concentrate on the case of a single adjoint hypermultiplet with a mass term and argue that the theory has a symmetry enlargement at mass M=1/(2r), where r is the $S^5$ radius. However, in order to have a well-defined localization locus it is necessary to rotate M onto the imaginary axis, breaking the enlarged symmetry. Based on our prescription, the imaginary mass values are physical and we show how the localized path integral is consistent with earlier results for 5D SYM in flat space. We then compute the free energy and the expectation value for a circular Wilson loop in the large N limit. The Wilson loop calculation shows a mass dependent constant rescaling between weak and strong coupling. The Wilson loop continued back to to the enlarged symmetry point is consistent with a supergravity computation for an M2 brane using the standard identification of the compactification radius and the 5D coupling. If we continue back to the physical regime and use this value of the mass to determine the compactification radius, then we find agreement between the SYM free energy and the corresponding supergravity calculation. We also verify numerically some of our analytic approximations.

Holographic Duality with a View Toward Many-Body Physics

Abstract: These are notes based on a series of lectures given at the KITP workshop Quantum Criticality and the AdS/CFT Correspondence in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion of string theory and of supersymmetry is avoided to the extent possible.

The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere

Abstract: Based on the construction by Hosomichi, Seong and Terashima we consider N = 1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation of the theory in flat space with deformation parameter r and this deformation preserves 8 supercharges. We calculate the full perturbative partition function as a function of $ {{{r} \left/ {{g_Y^2}} \right.}_M} $ , where $ {g_Y}_M $ is the Yang-Mills coupling, and the answer is given in terms of a matrix model. We perform the calculation using localization techniques. We also argue that in the large N-limit of this deformed 5D Yang-Mills theory this matrix model provides the leading contribution to the partition function and the rest is exponentially suppressed.

Supersymmetry on Curved Spaces and Holography

Abstract: We study superconformal and supersymmetric theories on Euclidean four- and threemanifolds with a view toward holographic applications. Preserved supersymmetry for asymptotically locally AdS solutions implies the existence of a (charged) “conformal Killing spinor” on the boundary. We study the geometry behind the existence of such spinors. We show in particular that, in dimension four, they exist on any complex manifold. This implies that a superconformal theory has at least one supercharge on any such space, if we allow for a background field (in general complex) for the R-symmetry. We also show that this is actually true for any supersymmetric theory with an R-symmetry. We also analyze the three-dimensional case and provide examples of supersymmetric theories on Sasaki spaces.

Superconformal partition functions and non-perturbative topological strings

Abstract: We propose a non-perturbative definition for refined topological strings. This can be used to compute the partition function of superconformal theories in 5 dimensions on squashed S5 and the superconformal index of a large number of 6 dimensional (2, 0) and (1, 0) theories, including that of N coincident M5 branes. The result can be expressed as an integral over the product of three combinations of topological string amplitudes. SL(3,Z) modular transformations acting by inverting the coupling constants of the refined topological string play a key role.

Exact results for five-dimensional superconformal field theories with gravity duals

Abstract: We apply the technique of supersymmetric localization to exactly compute the S 5 partition function of several large N superconformal field theories in five dimensions that have AdS6 duals in massive type IIA supergravity. The localization computations are performed in the non-renormalizable effective field theories obtained through relevant deformations of the UV superconformal field theories. We compare the S 5 free energy to a holographic computation of entanglement entropy in the AdS6 duals and find perfect agreement. In particular, we reproduce the N 5/2 scaling of the S 5 free energy that was expected from supergravity.