In theoretical physics, the Curtright field (named after Thomas Curtright)[1] is a tensor quantum field of mixed symmetry, whose gauge-invariant dynamics are dual to those of the general relativistic graviton in higher (D>4) spacetime dimensions.
Several difficulties arise when interactions of mixed symmetry fields are considered, but at least in situations involving an infinite number of such fields (notably string theory) these difficulties are not insurmountable.
[5] In four spacetime dimensions, the field is not dual to the graviton, if massless, but it can be used to describe massive, pure spin 2 quanta.
[7] The simplest example of the linearized theory is given by a rank three Lorentz tensor
whose indices carry the permutation symmetry of the Young diagram corresponding to the integer partition 3=2+1.
in D spacetime dimensions is bilinear in the field strength and its trace.
This action is gauge invariant, assuming there is zero net contribution from any boundaries, while the field strength itself is not.
The gauge transformation in question is given by where S and A are arbitrary symmetric and antisymmetric tensors, respectively.
An infinite family of mixed symmetry gauge fields arises, formally, in the zero tension limit of string theory,[8] especially if D>4.
Such mixed symmetry fields can also be used to provide alternate local descriptions for massive particles, either in the context of strings with nonzero tension, or else for individual particle quanta without reference to string theory.