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arXiv 2002.11466hep-th
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大质量四维阿贝尔2-形式理论：（反）手征超场方法的幂零对称性

Massive 4D Abelian 2-Form Theory: Nilpotent Symmetries from the (Anti-)Chiral Superfield Approach

S. Kumar, B. Chauhan, A. Tripathi, R. P. Malik

备注：
LaTeX file, 55 pages, minor changes in the title and text, version to appear in IJMPA
发表信息：
Int. J. Mod. Phys.} A 37 (2022) 2250003 (60 pages)
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摘要：

利用（反）手征超场方法（ACSA）得到了（3+1）维（4D）St $\ddot{u}$ ckelberg修正的有质量阿贝尔2-形式规范理论的Becchi-Rouet-Stora-Tyrons（BRST）形式的离壳幂零（反）BRST对称变换.我们执行完全类似的练习推导出的离壳幂零（反）co-BRST对称变换，太。在上述推导中，超场的对称不变限制起着非常重要的决定性作用。为了证明上述幂零对称性的神圣性，我们推广了我们的4D普通理论（定义在4D平坦Minkowski时空流形上）到其对应的（4，2）维超流形的（4，1）维（反）手征超级子流形，其由超空间坐标$Z^{M} = (x^μ,θ, \barθ ) $参数化，其中$x^μ( μ= 0,1,2,3 )$是玻色子坐标，一对格拉斯曼变量$(θ, \barθ)$是费米子：（$θ^{2} = \bar{θ^{2}} = 0, \,\,θ\,\barθ +\barθ\,θ= 0$）。我们目前的努力的一个新的观察是推导的Curci-Ferrari（CF）型限制的要求的对称不变性的耦合（但等效）拉格朗日密度为我们的理论框架内的ACSA BRST形式主义。我们还利用ACSA的标准技术来捕获的离壳幂零性和绝对反交换性的保守（反）BRST以及（反）共BRST收费。以一种微妙的方式，上述守恒电荷的绝对反对易性的证明也意味着对我们的理论存在适当的CF型限制。

英文摘要：

We derive the off-shell nilpotent (anti-)BRST symmetry transformations by exploiting the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism for the four (3+1)-dimensional (4D) St$\ddot{u}$ckelberg-modified massive Abelian 2-form gauge theory. We perform exactly similar kind of exercise for the derivation of the off-shell nilpotent (anti-)co-BRST symmetry transformations, too. In the above derivations, the symmetry invariant restrictions on the superfields play very important and decisive roles. To prove the sanctity of the above nilpotent symmetries, we generalize our 4D ordinary theory (defined on the 4D flat Minkowskian spacetime manifold) to its counterparts (4,1)-dimensional (anti-)chiral super sub-manifolds of the (4,2)-dimensional supermanifold which is parameterized by the superspace coordinates $Z^{M} = (x^μ,θ, \barθ ) $ where $x^μ( μ= 0,1,2,3 )$ are the bosonic coordinates and a pair of Grassmannian variables $(θ, \barθ)$ are fermionic: ($θ^{2} = \bar{θ^{2}} = 0, \,\,θ\,\barθ +\barθ\,θ= 0$) in nature. One of the novel observations of our present endeavor is the derivation of the Curci-Ferrari (CF) type restrictions from the requirement of the symmetry invariance of the coupled (but equivalent) Lagrangian densities for our theory within the framework of ACSA to BRST formalism. We also exploit the standard techniques of ACSA to capture the off-shell nilpotency and absolute anticommutativity of the conserved (anti-)BRST as well as the (anti-)co-BRST charges. In a subtle manner, the proof of the absolute anticommutativity of the above conserved charges also implies the existence of the appropriate CF-type restrictions on our theory.

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