57 research outputs found
M2-Branes and Fano 3-folds
A class of supersymmetric gauge theories arising from M2-branes probing
Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is
investigated. For each model, the toric data of the mesonic moduli space is
derived using the forward algorithm. The generators of the mesonic moduli space
are determined using Hilbert series. The spectrum of scaling dimensions for
chiral operators is computed.Comment: 128 pages, 39 figures, 42 table
The Hilbert Series of the One Instanton Moduli Space
The moduli space of k G-instantons on R^4 for a classical gauge group G is
known to be given by the Higgs branch of a supersymmetric gauge theory that
lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3,
these (3 + 1) dimensional gauge theories have N = 2 supersymmetry and can be
represented by quiver diagrams. The F and D term equations coincide with the
ADHM construction. The Hilbert series of the moduli spaces of one instanton for
classical gauge groups is easy to compute and turns out to take a particularly
simple form which is previously unknown. This allows for a G invariant
character expansion and hence easily generalisable for exceptional gauge
groups, where an ADHM construction is not known. The conjectures for
exceptional groups are further checked using some new techniques like sewing
relations in Hilbert Series. This is applied to Argyres-Seiberg dualities.Comment: 43 pages, 22 figure
Hilbert Series for Moduli Spaces of Two Instantons
The Hilbert Series (HS) of the moduli space of two G instantons on C^2, where
G is a simple gauge group, is studied in detail. For a given G, the moduli
space is a singular hyperKahler cone with a symmetry group U(2) \times G, where
U(2) is the natural symmetry group of C^2. Holomorphic functions on the moduli
space transform in irreducible representations of the symmetry group and hence
the Hilbert series admits a character expansion. For cases that G is a
classical group (of type A, B, C, or D), there is an ADHM construction which
allows us to compute the HS explicitly using a contour integral. For cases that
G is of E-type, recent index results allow for an explicit computation of the
HS. The character expansion can be expressed as an infinite sum which lives on
a Cartesian lattice that is generated by a small number of representations.
This structure persists for all G and allows for an explicit expressions of the
HS to all simple groups. For cases that G is of type G_2 or F_4, discrete
symmetries are enough to evaluate the HS exactly, even though neither ADHM
construction nor index is known for these cases.Comment: 53 pages, 9 tables, 24 figure
Phases of M2-brane Theories
We investigate different toric phases of 2+1 dimensional quiver gauge
theories arising from M2-branes probing toric Calabi-Yau 4 folds. A brane
tiling for each toric phase is presented. We apply the 'forward algorithm' to
obtain the toric data of the mesonic moduli space of vacua and exhibit the
equivalence between the vacua of different toric phases of a given singularity.
The structures of the Master space, the mesonic moduli space, and the baryonic
moduli space are examined in detail. We compute the Hilbert series and use them
to verify the toric dualities between different phases. The Hilbert series,
R-charges, and generators of the mesonic moduli space are matched between toric
phases.Comment: 60 pages, 28 figures, 6 tables. v2: minor correction
The ABCDEFG of Instantons and W-algebras
For arbitrary gauge groups, we check at the one-instanton level that the
Nekrasov partition function of pure N=2 super Yang-Mills is equal to the norm
of a certain coherent state of the corresponding W-algebra. For
non-simply-laced gauge groups, we confirm in particular that the coherent state
is in the twisted sector of a simply-laced W-algebra.Comment: 30 pages, 2 figures, v2: references added, explicit expression for
the W(E6) generators adde
Large N topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces
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