相关论文: Beyond Algebraic Solutions to Stringy Spacetime

Superstring compactifications have been vigorously studied for over four decades, and have flourished involving an active iterative feedback between physics and (complex) algebraic geometry. This led to an unprecedented wealth of…

We survey some algebraic geometric aspects of mirror symmetry and duality in string theory. Some applications of computer algebra to algebraic geometry and string theory are shortly reviewed.

The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\"{o}bner) methods are severely limited by algorithmic issues…

The most impressively prolific exploration of superstring models (aiming for our physical reality) has been focused on worldsheet-supersymmetric gauged linear sigma models and the closely associated complex-algebraic toric geometry. Mirror…

All known string theory models may be obtained as partial fermionization, projection and background Ans\"atze from the original, purely bosonic string theory. The latter theory in turn has been recently shown to describe a chirally and…

In a recent paper, algebraic descriptions for all non-relativistic spins were derived by elementary means directly from the Lie algebra $\specialorthogonalliealgebra{3}$, and a connection between spin and the geometry of Euclidean…

The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly…

Supersymmetry has been studied for over three decades by physicists, its superset even longer by mathematicians, and superspace has proven to be very useful both conceptually and in facilitating computations. However, the (1) necessary…

These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…

After many years, the deep nature of spacetime in string theory remains an enigma. In this letter we incorporate the concept of Born reciprocity in order to provide a new point of view on string theory in which spacetime is a derived…

String theory has already motivated, suggested, and sometimes well-nigh proved a number of interesting and sometimes unexpected mathematical results, such as mirror symmetry. A careful examination of the behavior of string propagation on…

We use mirror symmetry to establish the first concrete arena of spacetime topology change in string theory. In particular, we establish that the {\it quantum theories} based on certain nonlinear sigma models with topologically distinct…

We illustrate the various ways in which the algebraic framework of noncommutative geometry naturally captures the short-distance spacetime properties of string theory. We describe the noncommutative spacetime constructed from a vertex…

Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…

Enumerative Geometry is concerned with the number of solutions to a structured system of polynomial equations, when the structure comes from geometry. Enumerative real algebraic geometry studies real solutions to such systems, particularly…

The coupled Einstein-Yang-Mills equations on a time dependent axially symmetric spacetime are investigated, without a priori any conditions on the gauge field. There is numerical evidence for the existence of a regular solution with the…

We study string theory in supersymmetric time-dependent backgrounds. In the framework of general relativity, supersymmetry for spacetimes without flux implies the existence of a covariantly constant null vector, and a relatively simple form…

String theory is a quantum theory that reproduces the results of General Relativity at long distances but is completely different at short distances. Mathematically, string theory is based on a very new -- and little understood -- framework…

The Hilbert spaces of supersymmetric systems admit symmetries which are often related to the topology and geometry of the (target) field-space. Here, we study certain (2,2)-supersymmetric systems in 2-dimensional spacetime which are closely…

We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces…