We show that scale-invariant special Kähler geometries whose generic $\textit{r}$ dim abelian variety fiber is isomorphic (completely split) or isogenous (completely iso-split) as a complex torus to the product of $\textit{r}$ one-dimensional complex tori have constant $\textit{τ}$ modulus on the Coulomb branch, i.e. are isotrivial. These simple results are useful in organizing the classification of scale-invariant special Kähler geometries, which, in turn, is relevant to the classification of possible 4-dimensional $$ \mathcal{N} $$ = 2 supersymmetric superconformal field theories.

United States

Philip Argyres

Robert Moscrop

Souradeep Thakur

South Korea

Mitch Weaver

Completely (iso-)split scale-invariant Coulomb branch geometries are isotrivial

We study holographic solutions describing RG flows across dimensions from five-dimensional $$N=2$$ SCFT to SCFTs in three and two dimensions using matter-coupled (4) gauged supergravity with $$ISO(3)\times U(1)$$ gauge group. By performing topological twists implemented by (2), $$SO(2)\times SO(2)$$ and (3) gauge fields, we find a number of $$AdS_4\times H^2$$ and $$AdS_3\times H^3$$ solutions preserving eight and four supercharges. These geometries are identified with conformal fixed points in three and two dimensions, respectively. The corresponding flow solutions are obtained numerically and can be interpreted as black membranes and black strings in asymptotically $$AdS_6$$ space. In addition, we have constructed charged domain wall solutions with $$AdS_2\times S^3$$ and $$AdS_3\times S^2$$ slicing. These solutions are supported by a non-vanishing two-form field and describe conformal line and surface defects within the $$N=2$$ SCFT in five dimensions, respectively. All of these solutions can be uplifted to type IIB theory via consistent truncations on $$S^2\times \Sigma $$ with $$\Sigma $$ being a Riemann surface.

Thailand

Parinya Karndumri

Twisted compactifications and conformal defects from ISO(3) $$\times $$ U(1)

We study supersymmetric $$AdS_6$$ black holes from matter-coupled (4) gauged supergravity coupled to four vector multiplets with $$ISO(3)\times U(1)$$ gauge group. This gauged supergravity admits a maximally supersymmetric $$AdS_6$$ vacuum with $$SO(3)\subset ISO(3)$$ symmetry. We find a number of new supersymmetric $$AdS_2\times \mathcal {M}_4$$ solutions by performing topological twists along $$\mathcal {M}_4$$ . For $$\mathcal {M}_4$$ being a product of two Riemann surfaces $$\Sigma \times \widetilde{\Sigma }$$ , we perform a twist by $$SO(2)\times U(1)$$ gauge fields and find $$AdS_2\times \Sigma \times \widetilde{\Sigma }$$ solutions for at least one of the Riemann surface being negatively curved. For $$\mathcal {M}_4$$ being a Kahler four-cycle $$\mathcal {M}_{\text {K}4}$$ , a twist by $$SO(2)\times U(1)$$ gauge fields leads to $$AdS_2\times \mathcal {M}_{\text {K}4}^-$$ solutions for negatively curved $$\mathcal {M}_{\text {K}4}$$ . Finally, performing a twist by turning on (3) gauge fields in the case of $$\mathcal {M}_4$$ being a Cayley four-cycle $$\mathcal {M}_{\text {C}4}$$ also leads to $$AdS_2\times \mathcal {M}_{\text {C}4}^-$$ solutions for negatively curved $$\mathcal {M}_{\text {C}4}$$ . We give numerical black hole solutions interpolating between all of these $$AdS_2\times \mathcal {M}_4$$ near horizon geometries and the asymptotically locally $$AdS_6$$ vacuum. It is also possible to uplift all of these solutions to type IIB theory via consistent truncations on $$S^2\times \Sigma $$ leading to a new class of supersymmetric $$AdS_2\times \mathcal {M}_4\times S^2\times \Sigma $$ solutions.

Supersymmetric $$AdS_6$$ black holes from ISO(3) $$\times $$ U(1)

We investigate string amplitudes by using the partial modular transformation which we introduced in our previous works. This enables us to extract stringy threshold corrections from the full string amplitudes and interpret them in terms of the Wilsonian effective field theory in a natural way. We calculate mass shifts and wave function renormalizations for massless scalar fields on brane-antibrane systems. We find that the mass shift can be exponentially small and negative. We also propose a strategy for realizing a hierarchical mass spectrum on D-branes.

Japan

Satoshi Iso

Noriaki Kitazawa

Takao Suyama

Stringy threshold corrections in D-brane systems

We study a solution generating technique in supergravity which can be viewed as a generalised version of U-duality, taking solutions of type IIA supergravity on a 6-sphere with RR flux to new solutions of 11-dimensional supergravity. The new solutions are characterised by an underlying 6-algebra structure. Our construction provides an 11-dimensional uplift of four-dimensional ISO(7) gauged supergravity, using E 7 exceptional geometry techniques. We focus on an example where we start with the D2 solution in type IIA supergravity and construct a new   <math> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math>  $$ \frac{1}{2} $$ -BPS 11-dimensional solution.

Spain

Belgium

Chris Blair

Sofia Zhidkova

Generalised U-dual solutions via ISO(7) gauged supergravity

Extra-dimensional components of gauge fields in higher-dimensional gauge theories will play a role of the Higgs field and become tachyonic after Kaluza-Klein compactifications on internal spaces with (topologically nontrivial) gauge field backgrounds. Its condensation is then expected to break gauge symmetries spontaneously. But, contrary to the expectation, some models exhibit restoration of gauge symmetries. In this paper, by considering all the massive Kaluza-Klein excitations of gauge fields, we explicitly show that some of them indeed become massless at the minimum of the Higgs potential and restore (a part of) the gauge symmetries which are broken by gauge field backgrounds. We particularly consider compactifications on <math><msup><mi>S</mi><mn>2</mn></msup></math> with monopolelike fluxes and also on <math><mrow><msup><mrow><mi>CP</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> with instanton and monopolelike fluxes. In some cases, the gauge symmetry is fully restored, as argued in previous literatures. In other cases, there is a stable vacuum with a partial restoration of the gauge symmetry after Higgs condensation. Topological structure of the gauge field configurations prevent the gauge symmetries from being restored.

Gauge symmetry restoration by Higgs condensation in flux compactifications on coset spaces

We give a large class of new supersymmetric Janus solutions in dyonic ISO(7) maximal gauged supergravity encompassing all known solutions appearing recently. We consider SO(3) invariant sector in which the gauged supergravity admits four supersymmetric AdS4 vacua with N = 1, 1, 2, 3 unbroken supersymmetries and G 2, SU(3), SU(3) × U(1) and SO(4) symmetries, respectively. We find Janus solutions preserving N = 1, 2, 3 supersymmetries and interpolating between AdS4 vacua and the N = 8 SYM phase. These solutions can be interpreted as conformal interfaces between SYM and various conformal phases of the dual field theory in three dimensions. The solutions can also be embedded in massive type IIA theory by a consistent truncation on S 6. We also find a number of singular Janus solutions interpolating between N = 8 SYM or AdS4 vacua and singularities or between singular geometries. It turns out that, apart from the SYM phase on D2-branes, all the singularities arising in these solutions are unphysical in both four- and ten-dimensional frameworks.

Chawakorn Maneerat

Janus solutions from dyonic ISO(7) maximal gauged supergravity

“Axion-CMB scenario” is an interesting possibility to explain the temperature anisotropy of the cosmic microwave background (CMB) by primordial fluctuations of the QCD axion [S. Iso, K. Kawana, and K. Shimada, Phys. Rev. D 102, 103513 (2020)]. In this scenario, fluctuations of radiations are generated by an energy exchange between axions and radiations, which results in the correlation between the primordial axion fluctuations and the CMB anisotropies. Consequently, the cosmological observations stringently constrain a model of the axion and the early history of the universe. In particular, we need a large energy fraction <math><msub><mi>Ω</mi><mi>A</mi></msub></math> of the axion at the QCD phase transition, but it must become tiny at the present universe to suppress the isocurvature power spectrum. One of natural cosmological scenarios to realize such a situation is the thermal inflation which can sufficiently dilute the axion abundance. Thermal inflation occurs in various models. In this paper, we focus on a classically conformal (CC) <math><mi>B</mi><mo>−</mo><mi>L</mi></math> model with a QCD axion. In this model, the early universe undergoes a long supercooling era of the <math><mi>B</mi><mo>−</mo><mi>L</mi></math> and electroweak symmetries, and thermal inflation naturally occurs. Thus it can be a good candidate for the axion-CMB scenario. But the axion abundance at the QCD transition is shown to be insufficient in the original CC <math><mi>B</mi><mo>−</mo><mi>L</mi></math> model. To overcome the situation, we extend the model by introducing <math><mi>N</mi></math> scalar fields <math><mi>S</mi></math> (either massive or massless) and consider a novel cosmological history such that the <math><mi>O</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> and the <math><mi>B</mi><mo>−</mo><mi>L</mi></math> sectors evolve almost separately in the early universe. We find that all the necessary conditions for the axion-CMB scenario can be satisfied in some parameter regions for massless <math><mi>S</mi></math> fields, typically <math><mi>N</mi><mo>∼</mo><msup><mn>10</mn><mn>19</mn></msup></math> and the mass of <math><mi>B</mi><mo>−</mo><mi>L</mi></math> gauge boson around 5–10 TeV.

Kiyoharu Kawana

Kengo Shimada

Axion-CMB scenario in a supercooled universe

This is an extended version of the previous paper [S. Iso et al., Phys. Rev. D 103, 105010 (2021)] to study entanglement entropy (EE) of a half space in interacting field theories. In the previous paper, we have proposed a novel method to calculate EE based on the notion of <math><msub><mi>Z</mi><mi>M</mi></msub></math> gauge theory on Feynman diagrams, and shown that EE consists of two particular contributions, one from a renormalized two-point correlation function in the two-particle irreducible (2PI) formalism and another from interaction vertices. In this paper, we further investigate them in more general field theories and show that the non-Gaussian contributions from vertices can be interpreted as renormalized correlation functions of composite operators.

Takato Mori

Katsuta Sakai

Non-Gaussianity of entanglement entropy and correlations of composite operators

Entanglement entropy (EE) in interacting field theories has two important issues: renormalization of UV divergences and non-Gaussianity of the vacuum. In this paper, we investigate them in the framework of the two-particle irreducible formalism. In particular, we consider EE of a half space in an interacting scalar field theory. It is formulated as <math><msub><mi>Z</mi><mi>M</mi></msub></math> gauge theory on Feynman diagrams: <math><msub><mi>Z</mi><mi>M</mi></msub></math> fluxes are assigned on plaquettes and summed to obtain EE. Some configurations of fluxes are interpreted as twists of propagators and vertices. The former gives a Gaussian part of EE written in terms of a renormalized 2-point function while the latter reflects non-Gaussianity of the vacuum.