Multi - instantons, supersymmetry and topological field theories

In this letter we argue that instanton-dominated Green's functions in N=2 Super Yang-Mills theories can be equivalently computed either using the so-called constrained instanton method or making reference to the topological twisted version of the theory. Defining an appropriate BRST operator (as a supersymmetry plus a gauge variation), we also show that the expansion coefficients of the Seiberg-Witten effective action for the low-energy degrees of freedom can be written as integrals of total derivatives over the moduli space of self-dual gauge connections

Microscopic quantum superpotential in N=1 gauge theories

We consider the N=1 super Yang-Mills theory with gauge group U(N), adjoint chiral multiplet X and tree-level superpotential Tr W(X). We compute the quantum effective superpotential W_mic as a function of arbitrary off-shell boundary conditions at infinity for the scalar field X. This effective superpotential has a remarkable property: its critical points are in one-to-one correspondence with the full set of quantum vacua of the theory, providing in particular a unified picture of solutions with different ranks for the low energy gauge group. In this sense, W_mic is a good microscopic effective quantum superpotential for the theory. This property is not shared by other quantum effective superpotentials commonly used in the literature, like in the strong coupling approach or the glueball superpotentials. The result of this paper is a first step in extending Nekrasov's microscopic derivation of the Seiberg-Witten solution of N=2 super Yang-Mills theories to the realm of N=1 gauge theories.Comment: 23 pages, 1 figure; typos corrected, version to appear in JHE

SPADAS: A high-speed 3D single-photon camera for advanced driver assistance systems

Advanced Driver Assistance Systems (ADAS) are the most advanced technologies to fight road accidents. Within ADAS, an important role is played by radar- and lidar-based sensors, which are mostly employed for collision avoidance and adaptive cruise control. Nonetheless, they have a narrow field-of-view and a limited ability to detect and differentiate objects. Standard camera-based technologies (e.g. stereovision) could balance these weaknesses, but they are currently not able to fulfill all automotive requirements (distance range, accuracy, acquisition speed, and frame-rate). To this purpose, we developed an automotive-oriented CMOS single-photon camera for optical 3D ranging based on indirect time-of-flight (iTOF) measurements. Imagers based on Single-photon avalanche diode (SPAD) arrays offer higher sensitivity with respect to CCD/CMOS rangefinders, have inherent better time resolution, higher accuracy and better linearity. Moreover, iTOF requires neither high bandwidth electronics nor short-pulsed lasers, hence allowing the development of cost-effective systems. The CMOS SPAD sensor is based on 64 × 32 pixels, each able to process both 2D intensity-data and 3D depth-ranging information, with background suppression. Pixel-level memories allow fully parallel imaging and prevents motion artefacts (skew, wobble, motion blur) and partial exposure effects, which otherwise would hinder the detection of fast moving objects. The camera is housed in an aluminum case supporting a 12 mm F/1.4 C-mount imaging lens, with a 40°×20° field-of-view. The whole system is very rugged and compact and a perfect solution for vehicle’s cockpit, with dimensions of 80 mm × 45 mm × 70 mm, and less that 1 W consumption. To provide the required optical power (1.5 W, eye safe) and to allow fast (up to 25 MHz) modulation of the active illumination, we developed a modular laser source, based on five laser driver cards, with three 808 nm lasers each. We present the full characterization of the 3D automotive system, operated both at night and during daytime, in both indoor and outdoor, in real traffic, scenario. The achieved long-range (up to 45m), high dynamic-range (118 dB), highspeed (over 200 fps) 3D depth measurement, and high precision (better than 90 cm at 45 m), highlight the excellent performance of this CMOS SPAD camera for automotive applications. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only

Superlocalization formulas and supersymmetric Yang-Mills theories

By using supermanifold techniques we prove a generalization of the localization formula in equivariant cohomology which is suitable for studying supersymmetric Yang-Mills theories in terms of ADHM data. With these techniques one can compute the reduced partition functions of topological super Yang-Mills theory with 4, 8 or 16 supercharges. More generally, the superlocalization formula can be applied to any topological field theory in any number of dimensions.Comment: 22 pages, Latex2

Matone's Relation in the Presence of Gravitational Couplings

The prepotential in N=2 SUSY Yang-Mills theories enjoys remarkable properties. One of the most interesting is its relation to the coordinate on the quantum moduli space $u=$ that results into recursion equations for the coefficients of the prepotential due to instantons. In this work we show, with an explicit multi-instanton computation, that this relation holds true at arbitrary winding numbers. Even more interestingly we show that its validity extends to the case in which gravitational corrections are taken into account if the correlators are suitably modified. These results apply also to the cases in which matter in the fundamental and in the adjoint is included. We also check that the expressions we find satisfy the chiral ring relations for the gauge case and compute the first gravitational correction.Comment: 21 page

Glueball operators and the microscopic approach to N=1 gauge theories

We explain how to generalize Nekrasov's microscopic approach to N=2 gauge theories to the N=1 case, focusing on the typical example of the U(N) theory with one adjoint chiral multiplet X and an arbitrary polynomial tree-level superpotential Tr W(X). We provide a detailed analysis of the generalized glueball operators and a non-perturbative discussion of the Dijkgraaf-Vafa matrix model and of the generalized Konishi anomaly equations. We compute in particular the non-trivial quantum corrections to the Virasoro operators and algebra that generate these equations. We have performed explicit calculations up to two instantons, that involve the next-to-leading order corrections in Nekrasov's Omega-background.Comment: 38 pages, 1 figure and 1 appendix included; v2: typos and the list of references corrected, version to appear in JHE

N=2 SYM Action as a BRST Exact Term, Topological Yang Mills and Instantons

By constructing a nilpotent extended BRST operator \bs that involves the N=2 global supersymmetry transformations of one chirality, we show that the standard N=2 off-shell Super Yang Mills Action can be represented as an exact BRST term \bs \Psi, if the gauge fermion $\Psi$ is allowed to depend on the inverse powers of supersymmetry ghosts. By using this nonanalytical structure of the gauge fermion (via inverse powers of supersymmetry ghosts), we give field redefinitions in terms of composite fields of supersymmetry ghosts and N=2 fields and we show that Witten's topological Yang Mills theory can be obtained from the ordinary Euclidean N=2 Super Yang Mills theory directly by using such field redefinitions. In other words, TYM theory is obtained as a change of variables (without twisting). As a consequence it is found that physical and topological interpretations of N=2 SYM are intertwined together due to the requirement of analyticity of global SUSY ghosts. Moreover, when after an instanton inspired truncation of the model is used, we show that the given field redefinitions yield the Baulieu-Singer formulation of Topological Yang Mills.Comment: Latex, 1+15 pages. Published versio

Instantons on Quivers and Orientifolds

We compute the prepotential for gauge theories descending from ${\cal N}=4$ SYM via quiver projections and mass deformations. This accounts for gauge theories with product gauge groups and bifundamental matter. The case of massive orientifold gauge theories with gauge group SO/Sp is also described. In the case with no gravitational corrections the results are shown to be in agreement with Seiberg-Witten analysis and previous results in the literature.Comment: 28 pages, revised version, references added, some typos correcte

Multi instanton calculus on ALE spaces

We study SYM gauge theories living on ALE spaces. Using localization formulae we compute the prepotential (and its gravitational corrections) for SU(N) supersymmetric ${\cal N}=2, 2^*$ gauge theories on ALE spaces of the $A_n$ type. Furthermore we derive the Poincar\'{e} polynomial describing the homologies of the corresponding moduli spaces of self-dual gauge connections. From these results we extract the ${\cal N}=4$ partition function which is a modular form in agreement with the expectations of $SL(2,\Z)$ duality.Comment: 26 pages, few explanations added. version to appear in nucl.phy