Gauge vector field localization on a 3-brane placed in a warped transverse resolved conifold

Abstract

We have investigated the features of the gauge vector field in a braneworld scenario built as a warped product between a 3-brane and a 2-cycle of the resolved conifold. This scenario allowed us to study how the gauge field behaves when the transverse manifold evolves upon a geometric flow that controls the singularity at the origin. Also, since the transverse manifold has a cylindrical symmetry according to the 3-brane, this geometry can be regarded as a near brane correction of the stringlike branes. Indeed, by means of a new warp function and the angular metric component of the resolved conifold, the braneworld can exhibit a conical form near the origin as well as a regular behavior in that region. The analysis of the gauge field in this background has been carried out for the s-wave state and a normalizable massless mode was found. For the massive modes, the resolution parameter avoids an infinite well on the brane and controls the depth of the well and the height of the barrier around the brane. The massive modes are slightly changed near the brane but they agree with the stringlike spectrum for large distances.

U(1) gauge vector field on a codimension-2 brane

“…In a model of brane with codimension two, extra dimensions can be assumed to be both compact [20], or one of them is compact and another is non-compact [6,45,[47][48][49], or both non-compact [21], where the ansatz was supposed as…”

“…With a KK decomposition of the vector field and a dimension reduction, we will obtain the effective actions for the vector KK modes. It is easy to show that the effective action of the vector zero mode is also gauge invariant, while the ones for the massive KK modes are not without some mechanisms [42][43][44][45].…”

${\boldsymbol~K}$-fields domain wall

“…1983年, Rubakov和Shaposhnikov [4] 通过构造在具有无限大 额外维的五维平直时空背景下的畴壁解, 证明了手 征费米子可局域化在畴壁上, 这为无穷大额外维的 存在提供了一种可行的机制, 显然假设我们是生活 在一个高维时空中的畴壁上是合理的. 后来人们 通过考虑引力, 将Rubakov和Shaposhnikov的畴壁解 推广到弯曲时空中, 提出了厚膜模型, 发现各种物 质场都可以通过与厚膜的背景耦合而局域化在膜 上 [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . 在额外维理论提出以后人们将其应用到 各种模型并且成功地解决了很多物理疑难, 例如规 范层次问题 [20][21][22][23][24][25][26] 、宇宙学常数问题 [27][28][29][30][31][32][33] 以及暗物 质 [34][35][36] 等.…”

“…至此费米子已 通过这种机制成功地局域化在四维时空, 这就提供 了一种使得大额外维可能存在的机制. 类似的耦合 方式后来被广泛用来研究费米子在弯曲畴壁上的局 域化 [5,[8][9][10][11][12][13][14][15][16][17][18][19] . 接下来主要进行K-场畴壁解的构造, K-场是指 具有非正则动能项的标量场.…”

Localization and mass spectra of various matter fields on Weyl thin brane

“…In order to ensure that the zero mode of vector field can be localized on the brane, the case of generalized RS branes with more extra dimensions was considered [31,32], a dynamical mass term was included in gauge field localization [33,34], and in Refs. [35][36][37][38][39][40][41][42][43][44] the authors introduced the interaction with the background scalar field. Localization of the fermion zero mode on a brane is especially important.…”