11,127 research outputs found
Degenerate and Stable Yang-Mills-Higgs Pairs
In this paper, we introduce some notions on the pair consisting of a Chern
connection and a Higgs field closely related to the first and second variation
of Yang-Mills- Higgs functional, such as strong Yang-Mills-Higgs pair,
degenerate Yang-Mills-Higgs pair, stable Yang-Mills-Higgs pair. We investigate
some properties of such pairs
Kauffman polynomial from a generalized Yang-Yang function
For the fundamental representations of the simple Lie algebras of type
, and , we derive the braiding and fusion matrices from
the generalized Yang-Yang function and prove that the corresponding knot
invariants are Kauffman polynomial.Comment: 40 pages, 17 figures. arXiv admin note: text overlap with
arXiv:1312.176
Entanglement Entropy of with massless flavors at non-zero temperature
We consider backreacted coupled with massless
flavors introduced by D7-branes at non-zero temperature. The backreacted
geometry is in the Veneziano limit. The temperature of this system is related
to the event horizon at . Dividing one of the spatial directions into a
line segment with length , we will calculate the entanglement entropy
between the two subspaces. We study the behavior near the event horizon, and
finally find that there exists phase transition phenomenon near the event
horizon since the difference between the entanglement entropy of the connected
minimal surface and the disconnected one changes sign
Entanglement Entropy of with massive flavors
We consider backreacted coupled with massive flavors
introduced by D7-branes. The backreacted geometry is in the Veneziano limit
with fixed . By dividing one of the directions into a line segment
with length , we get two subspaces. Then we calculate the entanglement
entropy between them. With the method provided by Klebanov, Kutasov and
Murugan, we are able to find the cut-off independent part of the entanglement
entropy and finally find that this geometry shows no phase transition as the
case in pure
HOMFLY polynomial from a generalized Yang-Yang function
Starting from the free field realization of Kac-Moody Lie algebra, we define
a generalized Yang-Yang function. Then for the Lie algebra of type , we
derive braiding and fusion matrix by braiding the thimble from the generalized
Yang-Yang function. One can construct a knots invariant from the
braiding and fusion matrix. It is an isotropy invariant and obeys a skein
relation. From them, we show that the corresponding knots invariant is HOMFLY
polynomial.Comment: 25 pages, 14 figure
Intersecting branes and adding flavors to the Maldacena-Nunez background
We study adding flavors into the Maldacena-N\u{u}nez background. It is
achieved by introducing spacetime filling D9-branes or intersecting
D5-branes into the background with a wrapping D5-brane. Both D9-branes and
D5-branes can be spacetime filling from the 5D bulk point of view. At the
probe limit it corresponds to introducing non-chiral fundamental flavors into
the dual N=1 SYM. We propose a method to twist the fundamental flavor which has
to involve open string charge. It reflects the fact that coupling fundamental
matter to SYM in the dual string theory corresponds to adding an open string
sectorComment: 16 pages, no figures, use JHEP3.cls, more discussions were adde
Confinement of N=1 Super Yang-Mills from Supergravity
We calculate circular Wilson loop expectation value of pure
super Yang-Mills from the Klebanov-Strassker-Tseytlin solution of supergravity
and the proposed gauge/gravity duality. The calculation is performed
numerically via searching world-sheet minimal surface. It is shown that Wilson
loop exhibits area law for large radius which implies that super
Yang-Mills is confined at large distance or low energy scale. Meanwhile, Wilson
loop exhibits logarithmic behavior for small radius and it indicates
asymptotical freedom of super Yang-Mills at short distance or high
energy scale.Comment: use revtex4.cls, 8 pages, 4 eps fig
The "Ghost" Symmetry of the BKP hierarchy
In this paper, we systematically develop the "ghost" symmetry of the BKP
hierarchy through its actions on the Lax operator , the eigenfunctions and
the function. In this process, the spectral representation of the
eigenfunctions and a new potential are introduced by using squared
eigenfunction potential(SEP) of the BKP hierarchy. Moreover, the bilinear
identity of the constrained BKP hierarchy and Adler-Shiota-van-Moerbeke formula
of the BKP hierarchy are re-derived compactly by means of the spectral
representation and "ghost" symmetry.Comment: 23pages, to appear in Journal of Mathematical Physic
A graphical calculus for semi-groupal categories
Around the year 1988, Joyal and Street established a graphical calculus for
monoidal categories, which provides a firm foundation for many explorations of
graphical notations in mathematics and physics. For a deeper understanding of
their work, we consider a similar graphical calculus for semi-groupal
categories. We introduce two frameworks to formalize this graphical calculus, a
topological one based on the notion of a processive plane graph and a
combinatorial one based on the notion of a planarly ordered processive graph,
which serves as a combinatorial counterpart of a deformation class of
processive plane graphs. We demonstrate the equivalence of Joyal and Street's
graphical calculus and the theory of upward planar drawings. We introduce the
category of semi-tensor schemes, and give a construction of a free monoidal
category on a semi-tensor scheme. We deduce the unit convention as a kind of
quotient construction, and show an idea to generalize the unit convention.
Finally, we clarify the relation of the unit convention and Joyal and Street's
construction of a free monoidal category on a tensor scheme.Comment: 32 pages. To appear in Applied Categorical Structure
Combinatorics and algebra of tensor calculus
In this paper, motivated by the theory of operads and PROPs we reveal the
combinatorial nature of tensor calculus for strict tensor categories and show
that there exists a monad which is described by the coarse-graining of graphs
and characterizes the algebraic nature of tensor calculus.Comment: 88 page
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