arXiv subjects

Nicolo Piazzalunga

Publications and source records attributed to Nicolo Piazzalunga.

6 recordsLinked to original sources

arXiv2025

Coulomb branch localization, quasimaps, and surface counting in Calabi--Yau fourfolds

We present a string theoretic approach to surface counting in local Calabi--Yau fourfolds via supersymmetric localization in topologically twisted four-dimensional gauge theories. This approach is based on a spectral correspondence between PT1-stable pairs on local fourfolds and twisted quasimaps with fixed two-dimensional domain associated to the ADHM quiver, or, equivalently, ADHM sheaves. For local toric fourfolds, we derive a conjectural residue formula for the K-theoretic quasimap partition function via Coulomb branch localization. As a result, in this case, we obtain a conjectural prescription fixing all usual sign ambiguities in the equivariant computation of such invariants. We present some explicit computations for local P2, extending the results available in the literature, and describe the formalism in general. This is the first instance of Coulomb branch localization for a quasimap theory in the context of four-dimensional gauge theories.

math.AG↗

arXiv2025

Global magni$4$icence, or: 4G Networks

The global magnificent four theory is the homological version of a maximally supersymmetric $(8+1)$-dimensional gauge theory on a Calabi-Yau fourfold fibered over a circle. In the case of a toric fourfold we conjecture the formula for its twisted Witten index. String-theoretically we count the BPS states of a system of $D0$-$D2$-$D4$-$D6$-$D8$-branes on the Calabi-Yau fourfold in the presence of a large Neveu-Schwarz $B$-field. Mathematically, we develop the equivariant $K$-theoretic DT4 theory, by constructing the four-valent vertex with generic plane partition asymptotics. Physically, the vertex is a supersymmetric localization of a non-commutative gauge theory in $8+1$ dimensions.

hep-th↗

arXiv2023

From equivariant volumes to equivariant periods

We consider generalizations of equivariant volumes of abelian GIT quotients obtained as partition functions of 1d, 2d, and 3d supersymmetric GLSM on $S^1$, $D^2$ and $D^2 \times S^1$, respectively. We define these objects and study their dependence on equivariant parameters for non-compact toric Kähler quotients. We generalize the finite-difference equations (shift equations) obeyed by equivariant volumes to these partition functions. The partition functions are annihilated by differential/difference operators that represent equivariant quantum cohomology/K-theory relations of the target and the appearance of compact divisors in these relations plays a crucial role in the analysis of the non-equivariant limit. We show that the expansion in equivariant parameters contains information about genus-zero Gromov-Witten invariants of the target.

hep-th↗

arXiv2023

The one-legged K-theoretic vertex of fourfolds from 3d gauge theory

We present formulas for the K-theoretic Pandharipande-Thomas vertex of fourfolds, for the case of one non-trivial leg. They are obtained from computations in a three-dimensional supersymmetric gauge theory, where we identify the field content and boundary conditions that correspond to the vertex with tautological insertions.

hep-th↗

arXiv2022

Shifts of prepotentials (with an appendix by Michele Vergne)

We study the dynamics of supersymmetric theories in five dimensions obtained by compactifications of M-theory on a Calabi-Yau threefold X. For a compact X, this is determined by the geometry of X, in particular the Kahler class dependence of the volume of X determines the effective couplings of vector multiplets. Rigid supersymmetry emerges in the limit of divergent volume, prompting the study of the structure of Duistermaat-Heckman formula and its generalizations for non-compact toric Kahler manifolds. Our main tool is the set of finite-difference equations obeyed by equivariant volumes and their quantum versions. We also discuss a physical application of these equations in the context of seven-dimensional gauge theories, extending and clarifying our previous results. The appendix by M. Vergne provides an alternative local proof of the shift equation.

hep-th↗

arXiv2016

Towards a gauge theory interpretation of the real topological string

We consider the real topological string on certain non-compact toric Calabi-Yau three-folds X, in its physical realization describing an orientifold of type IIA on X with an O4-plane and a single D4-brane stuck on top. The orientifold can be regarded as a new kind of surface operator on the gauge theory with 8 supercharges arising from the singular geometry. We use the M-theory lift of this system to compute the real Gopakumar-Vafa invariants (describing wrapped M2-brane BPS states) for diverse geometries. We show that the real topological string amplitudes pick up certain signs across flop transitions, in a well-defined pattern consistent with continuity of the real BPS invariants. We further give some preliminary proposals of an intrinsically gauge theoretical description of the effect of the surface operator in the gauge theory partition function.

hep-th↗