相关论文: U-geometry : SL(5)

We discuss supersymmetric Yang-Mills theory dimensionally reduced to zero dimensions and evaluate the SU(2) and SU(3) partition functions by Monte Carlo methods. The exactly known SU(2) results are reproduced to very high precision. Our…

Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…

We summarize some previous work on SU(4) describing hadron representations and transformations as well as its noncompact 'counterpart' SU$*$(4) being the complex embedding of SL(2,$\mathbb{H}$). So after having related the 16-dim Dirac…

The effective dimension-5 operators can be induced by quantum gravity or inspired by string and M theories. They have important impacts on grand unified theories. We investigate the group theoretic nature of them for the well known E(6)…

Let $(M,g)$ be a Riemannian manifold, and $m$ be a second metric on $M$. We give expressions of $m$'s associated connection, and Riemann curvature tensor $R_m$, in terms of $R_g$ and certain combinations of covariant derivatives of $m$…

This thesis explores an exotic class of M-theory compactifications in which the compact manifold is taken to be a Calabi-Yau five-fold. The resulting effective theory is a one-dimensional N=2 super-mechanics model that exhibits peculiar…

We investigate supersymmetric $SU(4)_c\times SU(4)_{L+R}$ theory in 5 dimensions whose compactification on a $S^{(1)}/Z_2$ orbifold yields N=1 supersymmetric $SU(4)_c\times SU(2)_L\times SU(2)_R$ supplemented by a $\tl{U}(1)$ gauge…

We give a supersymmetric generalization of the sine algebra and the quantum algebra $U_{t}(sl(2))$. Making use of the $q$-pseudo-differential operators graded with a fermionic algebra, we obtain a supersymmetric extension of sine algebra.…

We systematically extend the elementary differential and Riemannian geometry of classical $\mathrm{U}(1)$-gauge theory to the noncommutative setting by combining recent advances in noncommutative Riemannian geometry with the theory of…

Differential geometry may be generalized to allow infinitesimals to any order. The purpose of the present contribution is to show that the theory so developed expands received geometrical ideas in an interesting way, rich in potential for…

We define an integral form of the deformed W-algebra of type gl_r, and construct its action on the K-theory groups of moduli spaces of rank r stable sheaves on a smooth projective surface S, under certain assumptions. Our construction…

The Grassmann envelope is used to find the $\mathcal{N}=1$ `superquasiconformal' algebra in $D=10+1$. The adjoint representation of this algebra is found to contain $\mathfrak{su}_{2,2}\oplus \mathfrak{u}_{1}\oplus \mathfrak{su}_{5}$ as a…

We study the three-dimensional effective action obtained by reducing eleven-dimensional supergravity with higher-derivative terms on a background solution including a warp-factor, an eight-dimensional compact manifold, and fluxes. The…

We derive the five-dimensional effective action of strongly coupled heterotic string theory for the complete (1,1) sector of the theory by performing a reduction, on a Calabi-Yau three-fold, of M-theory on S^1/Z_2. A crucial ingredient for…

The underlying even manifold of a super Riemann surface is a Riemann surface with a spinor valued differential form called gravitino. Consequently infinitesimal deformations of super Riemann surfaces are certain infinitesimal deformations…

The unit sphere $\mathbb S^3$ can be identified with the unitary group SU(2). Under this identification the unit sphere can be considered as a non-commutative Lie group. The commutation relations for the vector fields of the corresponding…

Recently Faddeev and Niemi proposed a low energy effective action for pure SU(2) Yang Mills theory in 4 dimension to describe its long distance physics. The effective action is O(3) $\sigma$ model with a mass parameter, a dimensionless…

We study Lie algebras endowed with an abelian complex structure which admit a symplectic form compatible with the complex structure. We prove that each of those Lie algebras is completely determined by a pair (U,H) where U is a complex…

The pure braid group \Gamma of a quadruply-punctured Riemann sphere acts on the SL(2,C)-moduli M of the representation variety of such sphere. The points in M are classified into \Gamma-orbits. We show that, in this case, the monodromy…

Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…