10 research outputs found
Equivalence of Carter diagrams
We introduce the equivalence relation ρ on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing l-cycles with l>4 to an equivalent Carter diagram containing only 4-cycles. Transforming one Carter diagram Γ₁ to another Carter diagram Γ₂ we can get a certain intermediate diagram Γ′ which is not necessarily a Carter diagram. Such an intermediate diagram is called a connection diagram. The relation ρ is the equivalence relation on the set of Carter diagrams and connection diagrams. The properties of connection and Carter diagrams are studied in this paper. The paper contains an alternative proof of Carter's classification of admissible diagrams
On Arnold's 14 `exceptional' N=2 superconformal gauge theories
We study the four-dimensional superconformal N=2 gauge theories engineered by
the Type IIB superstring on Arnold's 14 exceptional unimodal singularities
(a.k.a. Arnold's strange duality list), thus extending the methods of 1006.3435
to singularities which are not the direct sum of minimal ones. In particular,
we compute their BPS spectra in several `strongly coupled' chambers.
From the TBA side, we construct ten new periodic Y-systems, providing
additional evidence for the existence of a periodic Y-system for each isolated
quasi-homogeneous singularity with (more generally, for each N=2
superconformal theory with a finite BPS chamber whose chiral primaries have
dimensions of the form N/l).Comment: 73 pages, 7 figure
Categorical Tinkertoys for N=2 Gauge Theories
In view of classification of the quiver 4d N=2 supersymmetric gauge theories,
we discuss the characterization of the quivers with superpotential (Q,W)
associated to a N=2 QFT which, in some corner of its parameter space, looks
like a gauge theory with gauge group G. The basic idea is that the Abelian
category rep(Q,W) of (finite-dimensional) representations of the Jacobian
algebra should enjoy what we call the Ringel
property of type G; in particular, rep(Q,W) should contain a universal
`generic' subcategory, which depends only on the gauge group G, capturing the
universality of the gauge sector. There is a family of 'light' subcategories
, indexed by points , where
is a projective variety whose irreducible components are copies of
in one--to--one correspondence with the simple factors of G.
In particular, for a Gaiotto theory there is one such family of
subcategories, , for each maximal degeneration of
the corresponding surface , and the index variety may be identified
with the degenerate Gaiotto surface itself: generic light subcategories
correspond to cylinders, while closed-point subcategories to `fixtures'
(spheres with three punctures of various kinds) and higher-order
generalizations. The rules for `gluing' categories are more general that the
geometric gluing of surfaces, allowing for a few additional exceptional N=2
theories which are not of the Gaiotto class.Comment: 142 pages, 8 figures, 5 table
4d N=2 Gauge Theories and Quivers: the Non-Simply Laced Case
We construct the BPS quivers with superpotential for the 4d N=2 gauge
theories with non-simply laced Lie groups (B_n, C_n, F_4 and G_2). The
construction is inspired by the BIKMSV geometric engineering of these gauge
groups as non-split singular elliptic fibrations. From the categorical
viewpoint of arXiv:1203.6743, the fibration of the light category L(g) over the
(degenerate) Gaiotto curve has a monodromy given by the action of the outer
automorphism of the corresponding unfolded Lie algebra. In view of the
Katz--Vafa `matter from geometry' mechanism, the monodromic idea may be
extended to the construction of (Q, W) for SYM coupled to higher matter
representations. This is done through a construction we call specialization.Comment: 42 pages, 2 figure