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 $B_{n}$, $C_{n}$ and $D_{n}$, 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 AdS5×S5AdS_5 \times S^5 with massless flavors at non-zero temperature

We consider backreacted $AdS_5 \times S^5$ coupled with $N_f$ 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 $r_h$. Dividing one of the spatial directions into a line segment with length $l$, 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 AdS5×S5AdS_5 \times S^5 with massive flavors

We consider backreacted $AdS_5 \times S^5$ coupled with $N_f$ massive flavors introduced by D7-branes. The backreacted geometry is in the Veneziano limit with fixed $N_f/N_c$. By dividing one of the directions into a line segment with length $l$, 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 $AdS_5 \times S^5$

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 $A_{n}$, we derive braiding and fusion matrix by braiding the thimble from the generalized Yang-Yang function. One can construct a knots invariant $H(K)$ 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 ${\cal N}=1$ 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 ${\cal N}=1$ 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 ${\cal N}=1$ 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 $L$, the eigenfunctions and the $\tau$ 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