SYM on quotients of spheres and complex projective spaces

A bstract We introduce a generic procedure to reduce supersymmetric Yang-Mills (SYM) theory along the Hopf fiber of squashed S 2 r− 1 with U(1) r isometry, down ℂℙ base. This amounts fixing Killing vector v generating ⊂ rotation and dimensionally reducing either or another direction contained in . To perform such reduction we ℤ p quotient freely acting one two fibers. For fixed resulting manifolds / ≡ L ( p, ±1) are higher dimensional generalization lens spaces. In large limit shrinks effectively find theories living on base manifold. Starting from $$ \mathcal{N} N = SYM 3 5 compute perturbative partition functions and, limit, , respectively for 3. show how reductions inequivalent fibers give rise distinct Reducing gives an equivariant version Donaldson-Witten while other choice leads closely related Pestun’s 4 use our technique reproduce known results provide new particular how, at sum over fluxes arises flat connections ±1). Finally, 3, also comment factorization non simply connected manifolds.