7 problems

Let $M$ be a three-dimensional twisted torus, let $\widetilde{M}=M\times S^1$ be the corresponding trivial circle bundle with coordinates $x^\mu=(x^i,x^4)$, and let $p_\mu$ be the…

Sign conjecture. The left and right skew algebroids of $G$ differ by sign:

Let $V_k(z,\bar z)=: \exp\big({\,\mathrm{i}\,} k\cdot x(z,\bar z)\big):$ be a closed-string tachyon vertex operator in the linearisation of conformal field theory on flat space wit…

Uplift conjecture. The quasi-Poisson brackets above provide the uplift of the string $R$-flux algebra to M-theory. In the contraction limit $\lambda\to0$, $x^4$ becomes central and…

Let ${\cal X}^{1},{\cal X}^{2},{\cal X}^{3}$ denote the closed-string coordinate operators in an $R$-flux background, and let $R^{123}$ be the corresponding $R$-flux component. Wri…

Nonassociative phase-space algebra conjecture. After three T-dualities, the coordinates satisfy a nonassociative phase-space coordinate algebra whose Jacobiator reproduces this 3-b…

In a closed-string background with three-form flux, let $x^a$, $x^b$, and $x^c$ denote space-time coordinates, and let $[x^a,x^b,x^c]$ be their three-bracket. Three-bracket conject…