arXiv subjects

Hiroki Imai

Publications and source records attributed to Hiroki Imai.

3 recordsLinked to original sources

arXiv2026

Vacuum structure of a scalar field on a torus with uniform magnetic flux

We investigate the vacuum expectation value of a complex scalar field on a two-dimensional torus with quantized magnetic flux $M$. A characteristic feature of this system is the emergence of a critical area: when the area of the torus exceeds this critical value, the vacuum expectation value becomes nonvanishing. Furthermore, any nonzero vacuum expectation value necessarily exhibits nontrivial dependence on the coordinates of the torus. Employing the lowest-mode approximation, we find a single vacuum configuration for $M=1$, whereas two and six degenerate vacuum configurations arise for $M=2$ and $M=3$, respectively. We then analyze the symmetry properties of these vacuum configurations and determine whether they preserve or spontaneously break the symmetry of the underlying system.

hep-th↗

arXiv2024

Toward Realistic Models in $T^2/\mathbb{Z}_2$ Flux Compactification

We consider a six dimensional gauge theory compactified on $T^2/\mathbb{Z}_2$ with magnetic flux. The configurations of models are classified by winding numbers at the fixed points. Requiring the existence of generation numbers and Yukawa coupling, we see that allowed and forbidden configurations are described by geometry of winding numbers.

hep-ph↗

arXiv2022

Index and winding numbers on $T^2/\mathbb{Z}_N$ orbifolds with magnetic flux

We analyze the number of independent chiral zero modes and the winding numbers at the fixed points on $T^2/{\mathbb{Z}}_N$ ($N=2,3,4,6$) orbifolds with magnetic flux. In the case of $N=2$, we derive the index formula $n_{+}-n_{-}=M/2+(-V_{+}+V_{-})/4=M/2-V_{+}/2+1$ by using the trace formula, where $n_{\pm}$ are the numbers of the $\pm$ chiral zero modes and $V_{\pm}$ are the sums of the winding numbers at the fixed points on $T^2/{\mathbb{Z}}_2$. We also obtain the formula $n_{+}-n_{-}=M/N+(-V_{+}+V_{-})/(2N)=M/N-V_{+}/N+1$ for $N=3,4,6$ under an assumption.

hep-th↗