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Punctures and Dynamical Systems

Falk Hassler
(
- Pennsylvania U. and
- North Carolina U.
)
,
Jonathan J. Heckman
(
- Pennsylvania U.
)

Nov 10, 2017

47 pages

Published in:

Lett.Math.Phys. 109 (2019) 3, 449-495

Published: Aug 3, 2018

e-Print:

1711.03973 [hep-th]

DOI:

10.1007/s11005-018-1118-4 (publication)

View in:

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Abstract: (Springer)

With the aim of better understanding the class of 4D theories generated by compactifications of 6D superconformal field theories (SCFTs), we study the structure of

\mathcal {N}=1

supersymmetric punctures for class

\mathcal {S}_{\varGamma }

theories, namely the 6D SCFTs obtained from M5-branes probing an ADE singularity. For M5-branes probing a

\mathbb {C}^2 / \mathbb {Z}_{k}

singularity, the punctures are governed by a dynamical system in which evolution in time corresponds to motion to a neighboring node in an affine A-type quiver. Classification of punctures reduces to determining consistent initial conditions which produce periodic orbits. The study of this system is particularly tractable in the case of a single M5-brane. Even in this “simple” case, the solutions exhibit a remarkable level of complexity: Only specific rational values for the initial momenta lead to periodic orbits and small perturbations in these values lead to vastly different late-time behavior. Another difference from half BPS punctures of class

\mathcal {S}

theories includes the appearance of a continuous complex “zero mode” modulus in some puncture solutions. The construction of punctures with higher-order poles involves a related set of recursion relations. The resulting structures also generalize to systems with multiple M5-branes as well as probes of D- and E-type orbifold singularities.

Note:

v2: 52 pages, 7 figures, clarifications and references added

6D SCFTs
Punctures
Dynamical systems
4D SCFTs
orbifold: singularity
field theory: conformal
supersymmetry: 1
dynamical system
orbit
boundary condition

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Figures(6)

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