586 research outputs found
Strings and Super-Yang–Mills theory: the integrable story
Commentary on 'Long-range fraktur gfraktur l(n) integrable spin chains and plane-wave matrix theory' by N Beisert and T Klose, 2006 J. Stat. Mech. P07006
Yukawas, G-flux, and Spectral Covers from Resolved Calabi-Yau's
We use the resolution procedure of Esole and Yau arXiv:1107.0733 to study
Yukawa couplings, G-flux, and the emergence of spectral covers from
elliptically fibered Calabi-Yau's with a surface of A_4 singularities. We
provide a global description of the Esole-Yau resolution and use it to
explicitly compute Chern classes of the resolved 4-fold, proving the conjecture
of arXiv:0908.1784 for the Euler character in the process. We comment on the
physical implications of the surprising singular fibers in codimension 2 and 3
in arXiv:1107.0733 and emphasize a group theoretic interpretation based on the
A_4 weight lattice. We then construct explicit G-fluxes by brute force in one
of the 6 birationally equivalent Esole-Yau resolutions, quantize them
explicitly using our result for the second Chern class, and compute the
spectrum and flux-induced 3-brane charges, finding agreement with results and
conjectures of local models in all cases. Finally, we provide a precise
description of the spectral divisor formalism in this setting and sharpen the
procedure described in arXiv:1107.1718 in order to explicitly demonstrate how
the Higgs bundle spectral cover of the local model emerges from the resolved
Calabi-Yau geometry. Along the way, we demonstrate explicitly how the
quantization rules for fluxes in the local and global models are related.Comment: 68 pages (41 pages + 4 appendices
D-Brane Charges in Gepner Models
We construct Gepner models in terms of coset conformal field theories and
compute their twisted equivariant K-theories. These classify the D-brane
charges on the associated geometric backgrounds and therefore agree with the
topological K-theories. We show this agreement for various cases, in particular
the Fermat quintic.Comment: 25 pages, 2 figures. LaTeX. v2: typos and references corrected. v3:
reference adde
The Tate Form on Steroids: Resolution and Higher Codimension Fibers
F-theory on singular elliptically fibered Calabi-Yau four-folds provides a
setting to geometrically study four-dimensional N=1 supersymmetric gauge
theories, including matter and Yukawa couplings. The gauge degrees of freedom
arise from the codimension 1 singular loci, the matter and Yukawa couplings are
generated at enhanced singularities in higher codimension. We construct the
resolution of the singular Tate form for an elliptic Calabi-Yau four-fold with
an ADE type singularity in codimension 1 and study the structure of the fibers
in codimension 2 and 3. We determine the fibers in higher codimension which in
general are of Kodaira type along minimal singular loci, and are thus
consistent with the low energy gauge-theoretic intuition. Furthermore, we
provide a complementary description of the fibers in higher codimension, which
will also be applicable to non-minimal singularities. The irreducible
components in the fiber in codimension 2 correspond to weights of
representations of the ADE gauge group. These can split further in codimension
3 in a way that is consistent with the generation of Yukawa couplings. Applying
this reasoning, we then venture out to study non-minimal singularities, which
occur for A type along codimension 3, and for D and E also in codimension 2.
The fibers in this case are non-Kodaira, however some insight into these
singularities can be gained by considering the splitting of fiber components
along higher codimension, which are shown to be consistent with matter and
Yukawa couplings for the corresponding gauge groups.Comment: 75 pages, v2: clarifications and references added, JHEP versio
Six-dimensional Origin of SYM with Duality Defects
We study the topologically twisted compactification of the 6d
M5-brane theory on an elliptically fibered K\"ahler three-fold preserving two
supercharges. We show that upon reducing on the elliptic fiber, the 4d theory
is Super-Yang Mills, with varying complexified coupling ,
in the presence of defects. For abelian gauge group this agrees with the
so-called duality twisted theory, and we determine a non-abelian generalization
to . When the elliptic fibration is singular, the 4d theory contains 3d
walls (along the branch-cuts of ) and 2d surface defects, around which
the 4d theory undergoes duality transformations. Such
duality defects carry chiral fields, which from the 6d point of view arise as
modes of the two-form in the tensor multiplet. Each duality defect has a
flavor symmetry associated to it, which is encoded in the structure of the
singular elliptic fiber above the defect. Generically 2d surface defects will
intersect in points in 4d, where there is an enhanced flavor symmetry. The 6d
point of view provides a complete characterization of this 4d-3d-2d-0d
`Matroshka'-defect configuration.Comment: 62 pages, 4 figure
Exact expressions for quantum corrections to spinning strings
The one-loop worldsheet quantum corrections to the energy of spinning strings
on R x S^3 within AdS_5 x S^5 are reexamined. The explicit expansion in the
effective 't Hooft coupling \lambda'= \lambda/J^2 is rigorously derived. The
expansion contains both analytic and non-analytic terms in \lambda', as well as
exponential corrections. Furthermore, we pin down the origin of the terms that
are not captured by the quantum string Bethe ansatz, which only produces
analytic terms in \lambda'. It is shown that the analytic terms arise from
string fluctuations within the S^3, whereas the non-analytic and exponential
terms, which are not captured by the Bethe ansatz, originate from the
fluctuations in all directions within the supersymmetric sigma model on AdS_5 x
S^5. We also comment on the case of spinning string in AdS_3 x S^1.Comment: 12 pages, 1 figur
Towards mirror symmetry à la SYZ for generalized Calabi-Yau manifolds
Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror hat M, it is argued that the product M × hat M is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and hat M. The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric and non-geometric, are shown to agree with previous conjectures based on the requirement of mirror symmetry for Killing prepotentials. The fibers are conjectured to be destabilized by fluxes on generic SU(3) × SU(3) backgrounds, though they may survive at type-jumping points. T-dualizing the surviving fibers ensures the exchange of pure spinors under mirror symmetry
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