ASC Workshops

ASC Workshops

By The Arnold Sommerfeld Center for Theoretical Physics (ASC)Education
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ASC Workshops episodes

  • Orbifolds of 4d N=2 supersymmetric gauge theories
    After recalling how some 4d N=2 gauge theories arise from reductions of 6d N=(2,0) superconformal theories on
    a Riemann surface, I will discuss two discrete quotients with codimension 2 orbifold singularities. In the first
    case the orbifold acts by rotations around one plane of the 4d N=2 theory; this is related to a Gukov-Witten
    surface operator that imposes a monodromy around that plane. We deduce instanton partition functions in the
    presence of surface operators; interestingly, instantons can fractionalize. In the second case the orbifold acts by
    reflection on the 4d theory and the Riemann surface. We learn how boundaries are encoded in the AGT
    correspondence. We are led to consider 4d N=2 quiver theories where some vector multiplets live on a
    hemisphere and others on a projective space.
    1 hr 2 min
  • Vortices , wall-crossing and 3d Seiberg like dualities
    We explore 1d vortex dynamics of 3d supersymmetric Yang-Mills theories, as inferred from factorization of exact
    partition functions. Under Seiberg-like dualities, the 3d partition function must remain invariant, yet it is not a
    priori clear what should happen to the vortex dynamics. We observe that the 1d quivers for the vortices remain the
    same, and the net effect of the 3d duality map manifests as 1d Wall-Crossing phenomenon; Although the vortex
    number can shift along such duality maps, the ranks of the 1d quiver theory are unaffected, leading to a notion of
    fundamental vortices as basic building blocks for topological sectors. For Aharony-type duality, in particular,
    where one must supply extra chiral fields to couple with monopole operators on the dual side, 1d wall-crossings
    of an infinite number of vortex quiver theories are neatly and collectively encoded by 3d determinant of such
    extra chiral fields.
    58 min
  • E-string theory on Riemann surfaces
    We study compactifications of the 6d E-string theory, the theory of a small E_8 instanton, to four dimensions. In
    particular we identify N=1 field theories in four dimensions corresponding to compactifications on arbitrary
    Riemann surfaces with punctures and with arbitrary non-abelian flat connections as well as fluxes for the abelian
    sub-groups of the E_8 flavor symmetry. This sheds light on emergent symmetries in a number of 4d N=1 SCFTs
    (including the `E7 surprise' theory) as well as leads to new predictions for a large number of 4-dimensional
    exceptional dualities and symmetries.
    1 hr 6 min
  • Comments on Vertex Operator Algebras for N=2 SCFTs
    Every N=2 SCFT in four dimensions comes equipped with a vertex operator algebrathat encodes the spectrum
    and OPE coefficients of an infinite class of 1/4 BPS operators knownas Schur operators. I will discuss a number
    of results as well as open questions regarding thestructural properties of the VOAs that appear in this
    correspondence and their relationship to four-dimensional physics. I will discuss a proposal for how to recover of
    the Higgs branch ofvacua from the VOA and the consequences of this proposal for the behaviour of Schur superconformal
    indices under modular transformations. This leads to a surprising relationship between the a-type Weyl
    anomaly coefficient and the spectrum of surface operators in an N=2 SCFT.
    1 hr 10 min

About ASC Workshops

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The Arnold Sommerfeld Center for Theoretical Physics (ASC) in Munich regularly organizes workshops and conferences on special topics in theoretical physics, sometimes in collaboration with other…

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