2,403 research outputs found
Line defects and 5d instanton partition functions
We consider certain line defect operators in five-dimensional SUSY gauge
theories, whose interaction with the self-dual instantons is described by 1d
ADHM-like gauged quantum mechanics constructed by Tong and Wong. The partition
function in the presence of these operators is known to be a generating
function of BPS Wilson loops in skew symmetric tensor representations of the
gauge group. We calculate the partition function and explicitly prove that it
is a finite polynomial of the defect mass parameter , which is an essential
property of the defect operator and the Wilson loop generating function. The
relation between the line defect partition function and the qq-character
defined by N. Nekrasov is briefly discussed.Comment: 17 pages, 1 figure; typos fixed, references corrected; version to be
published in JHE
Line defects and 5d instanton partition functions
We consider certain line defect operators in five-dimensional SUSY gauge theories, whose interaction with the self-dual instantons is described by 1d ADHM-like gauged quantum mechanics constructed by Tong and Wong. The partition function in the presence of these operators is known to be a generating function of BPS Wilson loops in skew symmetric tensor representations of the gauge group. We calculate the partition function and explicitly prove that it is a finite polynomial of the defect mass parameter x, which is an essential property of the defect operator and the Wilson loop generating function. The relation between the line defect partition function and the qq-character defined by N . Nekrasov is briefly discussed.1112Nsciescopu
Topological strings and 5d T_N partition functions
We evaluate the Nekrasov partition function of 5d gauge theories engineered
by webs of 5-branes, using the refined topological vertex on the dual
Calabi-Yau threefolds. The theories include certain non-Lagrangian theories
such as the T_N theory. The refined topological vertex computation generically
contains contributions from decoupled M2-branes which are not charged under the
5d gauge symmetry engineered. We argue that, after eliminating them, the
refined topological string partition function agrees with the 5d Nekrasov
partition function. We explicitly check this for the T_3 theory as well as
Sp(1) gauge theories with N_f = 2, 3, 4 flavors. In particular, our method
leads to a new expression of the Sp(1) Nekrasov partition functions without any
contour integrals. We also develop prescriptions to calculate the partition
functions of theories obtained by Higgsing the T_N theory. We compute the
partition function of the E_7 theory via this prescription, and find the E_7
global symmetry enhancement. We finally discuss a potential application of the
refined topological vertex to non-toric web diagrams.Comment: 79 pages, 27 figures; v2: minor improvements, references adde
Supersymmetric vacua of mass-deformed M2-brane theory
We count the supersymmetric vacua of mass-deformed N=6 U(N)xU(N) Chern-Simons-matter theory by calculating the Witten index. When the Chern-Simons level k is 1, our result perfectly agrees with that from the gravity dual, given by partitions of N. For general k, our index generalizes partitions of N, including additional degrees. We also comment on non-relativistic superconformal theories constructed from this model.1130sciescopu
Towards Classification of 5d SCFTs: Single Gauge Node
We propose a number of apparently equivalent criteria necessary for the
consistency of a 5d SCFT in its Coulomb phase and use these criteria to
classify 5d SCFTs arising from a gauge theory with simple gauge group. These
criteria include the convergence of the 5-sphere partition function; the
positivity of particle masses and monopole string tensions; and the positive
definiteness of the metric in some region in the Coulomb branch. We find that
for large rank classical groups simple classes of SCFTs emerge where the bounds
on the matter content and the Chern-Simons level grow linearly with rank. For
classical groups of rank less than or equal to 8, our classification leads to
additional cases which do not fit in the large rank analysis. We also classify
the allowed matter content for all exceptional groups.Comment: 52 pages + appendix, 11 tables, 12 figure
- …