Siegenthaler showed that the correlation immunity m of a Boolean function of algebraic degree d of n variables satisfies m + d ≤ n; for a given set of input variables, this means that a high algebraic degree will restrict the maximum possible correlation immunity.
Siegenthaler's research showed that the correlation immunity (m) of a Boolean function with algebraic degree 'd' in 'n' variables is limited by the sum of 'm' and 'd', which must be less than or equal to 'n'.  This means that for a given set of input variables, a higher algebraic degree will restrict the maximum possible correlation immunity.