We present $N=2$ supersymmetric non-Abelian duality-symmetry between a tensor multiplet and an extra vector multiplet in $D=3+2$ dimensions. Our system has the Yang-Mills (YM) vector multiplet $(A_{\mu }{}^I,{\lambda }^I)$, a tensor-multiplet $(B_{\mu \nu }{}^I,{\chi }^I,{\phi }^I)$, and an extra vector multiplet $(C_{\mu }{}^I,{\rho }^I,{\sigma }^I)$. The index $I=1,2,\cdots ,\dim G$ is for the adjoint representation of a non-Abelian group G. The $A_{\mu }{}^I$ is the conventional YM gauge field, $B_{\mu \nu }{}^I$ is a non-Abelian tensor field, while ${\phi }^I$ and ${\sigma }^I$ are scalar fields. The ${\lambda }^I,{\chi }^I$ and ${\rho }^I$ are Majorana fermions in the 2 of $Sp(1)$. The $B_{\mu \nu }{}^I$ and $C_{\mu }{}^I\text{-}$fields have their respective field-strengths defined by $G_{\mu \nu \rho }{}^I\equiv +3D_{\lfloor \lceil \mu }B_{\nu \rho \rfloor \rceil }{}^I+3f^{IJK}F_{\lfloor \lceil \mu \nu }{}^{J}C_{\rho \rfloor \rceil }{}^K$ and $H_{\mu \nu }{}^I\equiv +2D_{\lfloor \lceil \mu }C_{\nu \rfloor \rceil }{}^I+mB_{\mu \nu }{}^I+f^{IJK}{\varphi }^{J}H_{\mu \nu }{}^K-f^{IJK}{\sigma }^{J}F_{\mu \nu }{}^K$. The duality relationship is $H_{\mu \nu }{}^I=(1/6)ϵ_{\mu \nu }{}^{\rho \sigma \tau }G_{\rho \sigma \tau }{}^I-(1/2)f^{IJK}({\bar{\lambda }}^J{\gamma }_{\mu \nu }{\chi }^K)$, with its super-partner relationships: ${\phi }^I=-{\sigma }^I,{\chi }^I=-{\rho }^I$. Since $H_{\sigma \tau }{}^I$ contains $mB_{\sigma \tau }{}^I$ linearly, this is a ‘massive’ self-dual relationship. Interestingly, the closure of supersymmetries shows the intrinsic global scale symmetry: ${\delta }_{\zeta }(B_{\mu \nu }{}^I,{\chi }^I,{\phi }^I,C_{\mu }{}^I,{\rho }^I,{\sigma }^I)=+m\zeta (B_{\mu \nu }{}^I,{\chi }^I,{\phi }^I,C_{\mu }{}^I,{\rho }^I,{\sigma }^I)$. By certain dimensional-reduction scheme into $D=2+2$, we show that self-dual supersymmetric tensor multiplet is generated. We deduce that our present theory in $D=3+2$ can serve as the underlying ‘Master Theory’ of a similar system in $D=2+2$.

我们提出 $ñ=2$ 张量多重态与额外向量多重态之间的超对称非阿贝尔对偶对称 $d=3+2$尺寸。我们的系统具有Yang-Mills（YM）矢量多重峰$（\mathrm{一种}_{\mu }{}^{\mathrm{一世}}，{\lambda }^{\mathrm{一世}}）$张量倍数 $（乙_{\mu \nu }{}^{\mathrm{一世}}，{\chi }^{\mathrm{一世}}，{\phi }^{\mathrm{一世}}）$，以及额外的向量多重 $（C_{\mu }{}^{\mathrm{一世}}，{\rho }^{\mathrm{一世}}，{\sigma }^{\mathrm{一世}}）$。指标$\mathrm{一世}=\mathrm{1个}，2，\cdots ，\mathrm{暗淡}G$用于非阿贝尔群G的伴随表示。的$\mathrm{一种}_{\mu }{}^{\mathrm{一世}}$ 是传统的YM量规领域， $乙_{\mu \nu }{}^{\mathrm{一世}}$是一个非阿贝尔张量场，而${\phi }^{\mathrm{一世}}$ 和 ${\sigma }^{\mathrm{一世}}$是标量字段。的${\lambda }^{\mathrm{一世}}，{\chi }^{\mathrm{一世}}$ 和 ${\rho }^{\mathrm{一世}}$是2中的马约拉纳费米子$\mathrm{小号}p（\mathrm{1个}）$。的$乙_{\mu \nu }{}^{\mathrm{一世}}$ 和 $C_{\mu }{}^{\mathrm{一世}}\text{--}$字段具有各自的字段强度，定义为 $G_{\mu \nu \rho }{}^{\mathrm{一世}}\equiv +3d_{\lfloor \lceil \mu }乙_{\nu \rho \rfloor \rceil }{}^{\mathrm{一世}}+3F^{\mathrm{一世}Ĵķ}F_{\lfloor \lceil \mu \nu }{}^{Ĵ}C_{\rho \rfloor \rceil }{}^{ķ}$ 和 $H_{\mu \nu }{}^{\mathrm{一世}}\equiv +2d_{\lfloor \lceil \mu }C_{\nu \rfloor \rceil }{}^{\mathrm{一世}}+米乙_{\mu \nu }{}^{\mathrm{一世}}+F^{\mathrm{一世}Ĵķ}{\varphi }^{Ĵ}H_{\mu \nu }{}^{ķ}-F^{\mathrm{一世}Ĵķ}{\sigma }^{Ĵ}F_{\mu \nu }{}^{ķ}$。对偶关系是$H_{\mu \nu }{}^{\mathrm{一世}}=（\mathrm{1个}/6）ϵ_{\mu \nu }{}^{\rho \sigma \tau }G_{\rho \sigma \tau }{}^{\mathrm{一世}}-（\mathrm{1个}/2）F^{\mathrm{一世}Ĵķ}（{\stackrel{〜}{\lambda }}^{Ĵ}{\gamma }_{\mu \nu }{\chi }^{ķ}）$，具有超级合作伙伴关系： ${\phi }^{\mathrm{一世}}=-{\sigma }^{\mathrm{一世}}，{\chi }^{\mathrm{一世}}=-{\rho }^{\mathrm{一世}}$。以来$H_{\sigma \tau }{}^{\mathrm{一世}}$ 包含 $米乙_{\sigma \tau }{}^{\mathrm{一世}}$线性地，这是一种“大量”的自我对偶关系。有趣的是，超对称的闭合显示出内在的全局尺度对称：${\delta }_{\zeta }（乙_{\mu \nu }{}^{\mathrm{一世}}，{\chi }^{\mathrm{一世}}，{\phi }^{\mathrm{一世}}，C_{\mu }{}^{\mathrm{一世}}，{\rho }^{\mathrm{一世}}，{\sigma }^{\mathrm{一世}}）=+米\zeta （乙_{\mu \nu }{}^{\mathrm{一世}}，{\chi }^{\mathrm{一世}}，{\phi }^{\mathrm{一世}}，C_{\mu }{}^{\mathrm{一世}}，{\rho }^{\mathrm{一世}}，{\sigma }^{\mathrm{一世}}）$。通过一定的降维方案$d=2+2$，我们证明了生成自对偶超对称张量多重峰。我们推断出我们目前的理论$d=3+2$ 可以用作类似系统中的基础“大师理论” $d=2+2$。