Abstract
M5 branes on a D-type ALE singularity display various phenomena that introduce additional massless degrees of freedom. The M5 branes are known to fractionate on a D-type singularity. Whenever two fractional M5 branes coincide, tensionless strings arise. Therefore, these systems do not admit a low-energy Lagrangian description. Focusing on the 6-dimensional mathcal{N} = (1, 0) world-volume theories on the M5 branes, the vacuum moduli space has two branches were either the scalar fields in the tensor multiplet or the scalars in the hypermultiplets acquire a non-trivial vacuum expectation value. As suggested in previous work, the Higgs branch may change drastically whenever a BPS-string becomes tensionless. Recently, magnetic quivers have been introduced with the aim to capture all Higgs branches over any point of the tensor branch. In this paper, the formalism is extended to Type IIA brane configurations involving O6 planes. Since the 6d mathcal{N} = (1, 0) theories are composed of orthosymplectic gauge groups, the derivation rules for the magnetic quiver in the presence of O6 planes have to be conjectured. This is achieved by analysing the 6d theories for a single M5 brane on a D-type singularity and deriving the magnetic quivers for the finite and infinite gauge coupling Higgs branch from a brane configuration. The validity of the proposed derivation rules is underpinned by deriving the associated Hasse diagram. For multiple M5 branes, the approach of this paper provides magnetic quivers for all Higgs branches over any point of the tensor branch. In particular, an interesting infinite gauge coupling transition is found that is related to the SO(8) non-Higgsable cluster.
Highlights
In contrast to lower dimensional theories, the gauge coupling in 6 dimensions is not a mere parameter, but inversely proportional to the vacuum expectation value of the scalar field in the tensor multiplet
For multiple M5 branes, the approach of this paper provides magnetic quivers for all Higgs branches over any point of the tensor branch
A unified analysis of the Higgs branch phases is possible by changing the phase of the Type IIA D6-D8-NS5 brane configuration to the phase where all D6 branes are suspended between D8 branes instead of NS5 branes
Summary
Consider M5 branes and a Dk ALE singularity C2/Dk−2 stretching the space-time dimensions as indicated in table 1. The singularity at the origin of C2/Dk−2 is localized in directions x7, x8, x9, and x10, and spans directions x0, x1, . The corresponding description in Type IIA is obtained by an identification as follows: the NS5 originates from the M5 which is point-like in the x10 direction. The Dk ALE space C2/Dk−2 in M-theory provides a local description of k coincident D6 branes on an O6− orientifold in Type IIA on flat space. X10, in which the singular origin of the ALE singularity is localised in, become the three directions transverse to the D6s and the direction of the M-theory circle. While for A-type singularities the number of fractions is just one, the M5 splits into two fractions on D-type orbifolds. N M5 on the D-type orbifold correspond to n pairs of two half NS5 branes in the dual Type IIA description. The different numbers of D6 branes follow from the charges of the orientifolds and the charge conservation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
