We propose mixed boundary conditions for 3d conformal gravity consistent with variational principle in its second-order formalism that admit the chiral $$\Lambda $$ - $$\mathfrak {bms}_4$$ algebra as their asymptotic symmetry algebra. This algebra is one of the four chiral $$\mathcal W$$ -algebra extensions of $$\mathfrak {so}(2,3)$$ and is a generalisation of the chiral $$\mathfrak {bms}_4$$ algebra responsible for soft theorems of graviton MHV amplitudes in $${\mathbb R}^{1,3}$$ gravity to the case of non-zero negative cosmological constant. The corresponding charges are shown to be finite and integrable, and realise this non-linear $${{\mathcal {W}}}$$ -algebra.

India

Nishant Gupta

Nemani Suryanarayana

Chiral $$\Lambda $$ - $$\mathfrak {bms}_4$$ symmetry of 3d conformal gravity

Generalising the chiral boundary conditions of <math><msup><mrow><mi>R</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msup></math> gravity for AdS$_{4}$ gravity, we derive chiral locally AdS$_{4}$ solutions in the Newman-Unti gauge consistent with a variational principle whose asymptotic symmetry algebra we show, to be an infinite-dimensional chiral extension of <math><mrow><mi>so</mi></mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math>. This symmetry algebra coincides with the chiral <math><msub><mrow><mi>bms</mi></mrow><mrow><mn>4</mn></mrow></msub></math> algebra in the flat space limit with the corresponding solutions mapping to the space of gravitational vacua in <math><msup><mrow><mi>R</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msup></math> gravity. We posit this symmetry algebra as the chiral version of recently discovered Λ-<math><msub><mrow><mi>bms</mi></mrow><mrow><mn>4</mn></mrow></msub></math> algebra. We propose line integral charges from the bulk AdS$_{4}$ gravity associated with this asymptotic symmetry algebra and show that they obey the semi-classical limit of a <math><mi>W</mi></math>-algebra. We derive this <math><mi>W</mi></math>-algebra for finite central charge c and level κ using associativity constraints of 2d CFT and find it to be isomorphic to one of quasi-superconformal algebra that existed in the literature.

Nemani V. Suryanarayana

A chiral Λ- symmetry of AdS Gravity

We show that there are four chiral   <math> <mi>W</mi> </math>  $$ \mathcal{W} $$ -algebra extensions of   <math> <mi>so</mi> <mfenced> <mn>2</mn> <mn>3</mn> </mfenced> </math>  $$ \mathfrak{so}\left(2,3\right) $$  algebra and construct them explicitly. We do this by a simple identification of each of the inequivalent embeddings of a copy of   <math> <mi>sl</mi> <mfenced> <mn>2</mn> <mi>ℝ</mi> </mfenced> </math>  $$ \mathfrak{sl}\left(2,\mathbb{R}\right) $$  in the   <math> <mi>so</mi> <mfenced> <mn>2</mn> <mn>3</mn> </mfenced> </math>  $$ \mathfrak{so}\left(2,3\right) $$  algebra and the maximal subalgebra   <math> <mi>h</mi> </math>  $$ \mathfrak{h} $$  that commutes with it. Then using the standard 2d chiral CFT techniques we find the corresponding   <math> <mi>W</mi> </math>  $$ \mathcal{W} $$ -algebra extensions. Two of the four resultant   <math> <mi>W</mi> </math>  $$ \mathcal{W} $$ -algebras are new, one of which may be thought of as the conformal   <math> <msub> <mi>bms</mi> <mn>3</mn> </msub> </math>  $$ {\mathfrak{bms}}_3 $$  algebra valid for finite values of its central charge.

All chiral   <math> <mi>W</mi> </math>  $$ \mathcal{W} $$ -algebra extensions of   <math> <mi>so</mi> <mfenced> <mn>2</mn> <mn>3</mn> </mfenced> </math>  $$ \mathfrak{so}\left(2,3\right) $$

We propose novel asymptotically locally flat boundary conditions for Einstein gravity without cosmological constant in four dimensions that are consistent with the variational principle. They allow for complex solutions that are asymptotically diffeomorphic to flat spacetimes under complexified diffeomorphisms. We show that the resultant asymptotic symmetries are an extension of the Poincaré algebra to a copy of Virasoro, a chiral <math><mi>sl</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>C</mi><mo>)</mo></math> current algebra along with two chiral <math><mi>u</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> currents. We posit that these bulk symmetries are direct analogs of the recently discovered chiral algebra symmetries of gravitational scattering amplitudes as celestial conformal field theory correlation functions.

Partha Paul

<math><mover><mrow><mi>s</mi><msub><mi>l</mi><mn>2</mn></msub></mrow><mo>^</mo></mover></math> symmetry of <math><msup><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msup></math> gravity

We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.

Constructing Carrollian CFTs

We point out a potential relevance between the Krein–Gupta–Bleuler (KGB) vacuum leading to a fully covariant quantum field theory for gravity in de Sitter (dS) spacetime and the observable smallness of the cosmological constant. This may provide a formulation of linear quantum gravity in a framework amenable to developing a more complete theory determining the value of the cosmological constant.

China

Hamed Pejhan

Japan

Kazuharu Bamba

Iran

Mohammad Enayati

Surena Rahbardehghan

A small non-vanishing cosmological constant from the Krein–Gupta–Bleuler vacuum

In this paper, vacuum expectation value (VEV) of the energy–momentum tensor for a conformally coupled scalar field in de Sitter space–time is investigated through the Krein–Gupta–Bleuler construction. This construction has already been successfully applied to the de Sitter minimally coupled massless scalar field and massless spin-2 field to obtain a causal and fully covariant quantum field on de Sitter background. We also consider the effects of boundary conditions. In this respect, Casimir energy–momentum tensor induced by Dirichlet boundary condition on a curved brane is evaluated.