Related papers: Loop Space Formalism and K-Theoretic Quantum Serre…
The fermion propagator is derived in detail from the model of fermion coupled to loop quantum gravity. As an ingredient of the propagator, the vacuum state is defined as the ground state of some effective fermion Hamiltonian under the…
We show that for any minuscule or cominuscule homogeneous space X, the Gromov-Witten varieties of degree d curves passing through three general points of X are rational or empty for any d. Applying techniques of A. Buch and L. Mihalcea to…
We study the quantum sheaf cohomology of flag manifolds with deformations of the tangent bundle and use the ring structure to derive how the deformation transforms under the biholomorphic duality of flag manifolds. Realized as the OPE ring…
Inspired by the long wave-length limit of topological M-theory, which re-constructs the theory of $3+1$D gravity in the self-dual variables' formulation, we conjecture the existence of a duality between Hilbert spaces, the ${\bf…
Using a construction derived from the descending central series of the free groups, we produce filtrations by infinite loop spaces of the classical infinite loop spaces $BSU$, $BU$, $BSO$, $BO$, $BSp$, $BGL_{\infty}(R)^{+}$ and…
We extend useful properties of the $H\to\gamma\gamma$ unintegrated dual amplitudes from one- to two-loop level, using the Loop-Tree Duality formalism. In particular, we show that the universality of the functional form -- regardless of the…
General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or…
We discuss the duality theorem, which provides a relation between loop integrals and phase space integrals. We rederive the duality relation for the one-loop case and extend it to two and higher-order loops. We explicitly show its…
We give a diagrammatic presentation in terms of generators mod relations of the representation category of $U_q(\mathfrak{sl}_n)$. More precisely, we produce all the relations among $\rm{SL}_n$-webs, thus describing the full subcategory…
Let $K$ be a local field with algebraically closed residue field and $X_K$ a torsor under an elliptic curve $J_K$ over $K$. Let $X$ be a proper minimal regular model of $X_K$ over the ring of integers of $K$ and $J$ the identity component…
Given a closed symplectic manifold $X$, we construct Gromov-Witten-type invariants valued both in (complex) $K$-theory and in any complex-oriented cohomology theory $\mathbb{K}$ which is $K_p(n)$-local for some Morava $K$-theory $K_p(n)$.…
We show that the classification of the symmetric spaces can be achieved by K-theoretical methods. We focus on Hermitian symmetric spaces of non-compact type, and define K-theory for JB*-triples along the lines of C*-theory. K-groups have to…
We introduce a notion of generalized Serre duality on a Hom-finite Krull-Schmidt triangulated category $\mathcal{T}$. This duality induces the generalized Serre functor on $\mathcal{T}$, which is a linear triangle equivalence between two…
We show a new neutral-fermionic presentation of Ikeda-Naruse's $K$-theoretic $Q$-functions, which represent a Schubert class in the $K$-theory of coherent sheaves on the Lagrangian Grassmannian. Our presentation provides a simple…
We prove an identity relating the product of two opposite Schubert varieties in the (equivariant) quantum K-theory ring of a cominuscule flag variety to the minimal degree of a rational curve connecting the Schubert varieties. We deduce…
We prove genus $g$ invariants in quantum $K$-theory are determined by genus zero invariants of a smooth stack in the spirit of K.~Costello's result in Gromov--Witten theory.
We construct the Schubert basis of the torus-equivariant K-homology of the affine Grassmannian of a simple algebraic group G, using the K-theoretic NilHecke ring of Kostant and Kumar. This is the K-theoretic analogue of a construction of…
Loop-tree duality allows to express virtual contributions in terms of phase-space integrals, thus leading to a direct comparison with real radiation terms. In this talk, we review the basis of the method and describe its application to…
This paper explains the conjectured algebraic duality between genus zero Gromov-Witten theory and genus zero "Closed String topology". This duality in another perspective is discussed on page 87 of the book "Frobenius manifold, quantum…
We study two aspects of fermionic T-duality: the duality in purely fermionic sigma models exploring the possible obstructions and the extension of the T-duality beyond classical approximation. We consider fermionic sigma models as coset…