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Register a new user$tau_{RR}$ minimization in presence of hypermultiplets
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We compute $tau_{RR}$ minimization in gauged supergravity for M-theory and String Theory truncations with both massless and massive vector multiplets. We explicitly compute, as anticipated in cite{Amariti:2015ybz}, that massive vector fields at the vacuum require the introduction of a constraint through a Lagrange multiplier. We illustrate this explicitly in two examples, namely the $U(1)^2$-invariant truncation dual to the mABJM model and the ISO(7) truncation in massive IIA, the latter being a theory with both electric and magnetic gauging. We revisit the vacuum constraints at $AdS_4$ and show how the supergravity analysis matches the results of the field theory dual computation.
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Building on the five-dimensional constructions in hep-th/0601177, we provide a unified description of four-dimensional N = 2 superconformal off-shell multiplets in projective superspace, including a realization in terms of N = 1 superfields. In particular, superconformal polar multiplets are consistently defined for the first time. We present new 4D N = 2 superconformal sigma-models described by polar multiplets. Such sigma-models realize general superconformal couplings in projective superspace, but involve an infinite tale of auxiliary N = 1 superfields. The auxiliaries should be eliminated by solving infinitely many algebraic nonlinear equations, and this is a nontrivial technical problem. We argue that the latter can be avoided by making use of supersymmetry considerations. All information about the resulting superconformal model (and hence the associated superconformal cone) is encoded in the so-called canonical coordinate system for a Kaehler metric, which was introduced by Bochner and Calabi in the late 1940s.
We consider resolutions of codimension-two enhanced singularities from $SO(12)$ to $E_7$ and from $E_7$ to $E_8$ in six-dimensional F-theory, where a half-hypermultiplet arises for generic complex structures achieving them. The exceptional fibers at the enhanced point exhibit different structures depending on how the colliding 7-brane approaches the stack of gauge 7-branes, as previously observed by Morrison and Taylor in the case of the enhancement from $SU(6)$ to $E_6$. When the colliding brane approaches them as $O(s)$, where $s$ is the coordinate of the base space along the gauge 7-branes, the resolution process ends up with fewer exceptional fibers than naively expected from the Kodaira classification, with a non-Dynkin intersection matrix including half-integral intersection numbers. We confirm that the exceptional fibers at the enhanced point form extremal rays of the cone of the positive weights of the relevant pseudo-real representation, explaining why a half-hypermultiplet arises there. By altering the ordering of the singularities blown up in the process, we obtain, for both $SO(12)rightarrow E_7$ and $E_7rightarrow E_8$, the intersection diagram on every other row of the corresponding box graphs. We present detailed derivations of the intersection diagrams of the exceptional fibers at the singularity enhanced points by examining how an exceptional curve is lifted up on the chart arising due to the subsequent blowing-up process. When the colliding brane approaches the stack of branes as $O(s^2)$, we obtain additional conifold singularity at the enhanced point, which completes the full Dynkin diagram of the enhanced group as was found previously.
We construct six-dimensional superconformal models with non-abelian tensor and hypermultiplets. They describe the field content of (2,0) theories, coupled to (1,0) vector multiplets. The latter are part of the non-abelian gauge structure that also includes non-dynamical three- and four-forms. The hypermultiplets are described by gauged nonlinear sigma models with a hyper-Kaehler cone target space. We also address the question of constraints in these models and show that their resolution requires the inclusion of abelian factors. These provide couplings that were previously considered for anomaly cancellations with abelian tensor multiplets and resulted in the selection of ADE gauge groups.
We study partial supersymmetry breaking from ${cal N}=2$ to ${cal N}=1$ by adding non-linear terms to the ${cal N}=2$ supersymmetry transformations. By exploiting the necessary existence of a deformed supersymmetry algebra for partial breaking to occur, we systematically use ${cal N}=2$ projective superspace with central charges to provide a streamlined setup. For deformed ${cal O}(2)$ and ${cal O}(4)$ hypermultiplets, besides reproducing known results, we describe new models exhibiting partial supersymmetry breaking with and without higher-derivative interactions.
As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) of strong-coupling expansion of non-planar corrections in $mathcal N=2$ 4d superconformal models we consider two special theories with gauge groups $SU(N)$ and $Sp(2N)$. They contain $N$-independent numbers of hypermultiplets in rank 2 antisymmetric and fundamental representations and are planar-equivalent to the corresponding $mathcal N=4$ SYM theories. These $mathcal N=2$ theories can be realised on a system of $N$ D3-branes with a finite number of D7-branes and O7-plane; the dual string theories should be particular orientifolds of $AdS_5times S^5$ superstring. Starting with the localization matrix model representation for the $mathcal N=2$ partition function on $S^4$ we find exact differential relations between the $1/N$ terms in the corresponding free energy $F$ and the $frac{1}{2}$-BPS Wilson loop expectation value $langlemathcal Wrangle$ and also compute their large t Hooft coupling ($lambda gg 1$) expansions. The structure of these expansions is different from the previously studied models without fundamental hypermultiplets. In the more tractable $Sp(2N)$ case we find an exact resummed expression for the leading strong coupling terms at each order in the $1/N$ expansion. We also determine the exponentially suppressed at large $lambda$ contributions to the non-planar corrections to $F$ and $langlemathcal Wrangle$ and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.
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