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Register a new user$mathcal{I}$/$c$-Extremization in M/F-Duality
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We study the holographic dual to $c$-extremization for 2d $(0,2)$ superconformal field theories (SCFTs) that have an AdS$_3$ dual realized in Type IIB with varying axio-dilaton, i.e. F-theory. M/F-duality implies that such AdS$_3$ solutions can be mapped to AdS$_2$ solutions in M-theory, which are holographically dual to superconformal quantum mechanics (SCQM), obtained by dimensional reduction of the 2d SCFTs. We analyze the corresponding map between holographic $c$-extremization in F-theory and $mathcal{I}$-extremization in M-theory, where in general the latter receives corrections relative to the F-theory result.
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We explore higher-form symmetries of M- and F-theory compactified on elliptic fibrations, determined by the topology of their asymptotic boundaries. The underlying geometric structures are shown to be equivalent to known characterizations of the gauge group topology in F-theory via Mordell--Weil torsion and string junctions. We further study dimensional reductions of the 11d Chern--Simons term in the presence of torsional boundary $G_4$-fluxes, which encode background gauge fields of center 1-form symmetries in the lower-dimensional effective gauge theory. We find contributions that can be interpreted as t Hooft anomalies involving the 1-form symmetry which originate from a fractionalization of the instanton number of non-Abelian gauge theories in F-/M-theory compactifications to 8d/7d and 6d/5d.
We consider $d=3$, $mathcal{N}=2$ gauge theories arising on membranes sitting at the apex of an arbitrary toric Calabi-Yau 4-fold cone singularity that are then further compactified on a Riemann surface, $Sigma_g$, with a topological twist that preserves two supersymmetries. If the theories flow to a superconformal quantum mechanics in the infrared, then they have a $D=11$ supergravity dual of the form AdS$_2times Y_9$, with electric four-form flux and where $Y_9$ is topologically a fibration of a Sasakian $Y_7$ over $Sigma_g$. These $D=11$ solutions are also expected to arise as the near horizon limit of magnetically charged black holes in AdS$_4times Y_7$, with a Sasaki-Einstein metric on $Y_7$. We show that an off-shell entropy function for the dual AdS$_2$ solutions may be computed using the toric data and Kahler class parameters of the Calabi-Yau 4-fold, that are encoded in a master volume, as well as a set of integers that determine the fibration of $Y_7$ over $Sigma_g$ and a Kahler class parameter for $Sigma_g$. We also discuss the class of supersymmetric AdS$_3times Y_7$ solutions of type IIB supergravity with five-form flux only in the case that $Y_7$ is toric, and show how the off-shell central charge of the dual field theory can be obtained from the toric data. We illustrate with several examples, finding agreement both with explicit supergravity solutions as well as with some known field theory results concerning ${cal I}$-extremization.
We show that if $R$ is a two dimensional standard graded ring (with the graded maximal ideal ${bf m}$) of characteristic $p>0$ and $Isubset R$ is a graded ideal with $ell(R/I) <infty$ then the $F$-threshold $c^I({bf m})$ can be expressed in terms of a strong HN (Harder-Narasimahan) slope of the canonical syzygy bundle on $mbox{Proj}~R$. Thus $c^I({bf m})$ is a rational number. This gives us a well defined notion, of the $F$-threshold $c^I({bf m})$ in characteristic $0$, in terms of a HN slope of the syzygy bundle on $mbox{Proj}~R$. This generalizes our earlier result (in [TrW]) where we have shown that if $I$ has homogeneous generators of the same degree, then the $F$-threshold $c^I({bf m})$ is expressed in terms of the minimal strong HN slope (in char $p$) and in terms of the minimal HN slope (in char $0$), respectively, of the canonical syzygy bundle on $mbox{Proj}~R$. Here we also prove that, for a given pair $(R, I)$ over a field of characteristic $0$, if $({bf m}_p, I_p)$ is a reduction mod $p$ of $({bf m}, I)$ then $c^{I_p}({bf m}_p) eq c^I_{infty}({bf m})$ implies $c^{I_p}({bf m}_p)$ has $p$ in the denominator, for almost all $p$.
Similarly to the bosonic Liouville theory, the $mathcal{N}=2$ supersymmetric Liouville theory was conjectured to be equipped with the duality that exchanges the superpotential and the Kahler potential. The conjectured duality, however, seems to suffer from a mismatch of the preserved symmetries. More than fifteen years ago, when I was a student, my supervisor Tohru Eguchi gave a beautiful resolution of the puzzle when the supersymmetry is enhanced to $mathcal{N}=4$ based on his insight into the underlying geometric structure of the $A_1$ singularity. I will review his unpublished but insightful idea and present our attempts to extend it to more general cases.
In this article, we seek exact charged spherically symmetric black holes (BHs) with considering $f(mathcal{R})$ gravitational theory. These BHs are characterized by convolution and error functions. Those two functions depend on a constant of integration which is responsible to make such a solution deviate from the Einstein general relativity (GR). The error function which constitutes the charge potential of the Maxwell field depends on the constant of integration and when this constant is vanishing we can not reproduce the Reissner-Nordstrom BH in the lower order of $f(mathcal{R})$. This means that we can not reproduce Reissner-Nordstrom BH in lower-order-curvature theory, i.e., in GR limit $f(mathcal{R})=mathcal{R}$, we can not get the well known charged BH. We study the physical properties of these BHs and show that it is asymptotically approached as a flat spacetime or approach AdS/dS spacetime. Also, we calculate the invariants of the BHS and show that the singularities are milder than those of BHs of GR. Additionally, we derive the stability condition through the use of geodesic deviation. Moreover, we study the thermodynamics of our BH and investigate the impact of the higher-order-curvature theory. Finally, we show that all the BHs are stable and have radial speed equal to one through the use of odd-type mode.
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