So I have what might be a fairly basic question, but my understanding that in the quantization of the the string, or the 1-brane, there are conditions on the number of spacetime dimensions to ensure that the Lorentz algebra still holds. For the bosonic string we have D=26 and for the superstring we have D=10.
Now I know that an equivalent condition on the critical dimension comes up by requiring that the conformal anomaly vanish. This is the prelude to my question: Are there any similar or equivalent restrictions on the number of spacetime dimensions are come up in the quantizing more general branes? Is it only the string because only the worldsheet theory has conformal invariance that we want to ensure holds in the quantized theory? If this statement is equivalent to the Lorentz algebra closing, why for a general p-brane do we not need to impose any conditions on the dimensions for this to hold?