25 problems

Higher-spin theories on twistor space are built from vector bundles and their associated curvature forms; their one-loop anomaly is governed by the index…

Let $U(N)_{k}\times U(N+M)_{-k}$ denote the ABJ theory, with $N$ finite and with $M$ and $k$ taken large. ABJ/Vasiliev duality conjecture. In this limit, the theory is dual to the…

A higher-spin field of spin $s$ is a field represented by a symmetric $s$-tensor, and the free theory has abelian gauge symmetries. For $s=3$, the higher-spin tower conjecture. all…

Consider the large-$N$ Chern–Simons gauge theory with fundamental fermions and its dual $SU(N_b)$ critical bosonic theory, in the limits and fixed ’t Hooft couplings described abov…

Let $J_{(s_i,q_i)}$, $J'_{(s_i,q_i)}$, and $J”_{(s_i,q_i)}$ denote conserved currents with spin and label data $(s_i,q_i)$, and let $\bar{J}'_{(s_2,q_2)}$ denote the barred current…

Higher-spin gauge theories are theories of fields with arbitrarily large spin, and the tensionless limit is the regime of string theory in which the string tension vanishes. Higher…

Let a large-$N$ conformal field theory have “single-trace” operators, and let $\Delta_{gap}$ be a parametrically large number. HPPS conjecture. For the CFT to have a local AdS dual…

The fractional quantum Hall effect has an area-preserving-diffeomorphism symmetry whose quantum realization involves the Girvin-Macdonald-Platzman algebra. The Magnetoroton is a sp…

The regular boson and critical boson theories are dual to the critical fermion and regular fermion theories, respectively. Boson–fermion duality conjecture. The regular boson/criti…

Classical Regge growth conjecture. The S-matrix of every physically acceptable classical theory never grows faster than $s^2$ at fixed $t$, at all physical values of momenta and fo…

Spin-locality conjecture. The concept of spin-local theories of infinite sets of fields is just a proper substitute for that of local theories describing finite collections of fiel…

Let Vasiliev's higher spin gauge theory be formulated on $AdS_4$, and let an $O(N)$ Vector Model denote the corresponding conformal vector model with global orthogonal symmetry. Va…

A $B_p$ Coxeter higher-spin model is a higher-spin system associated with the rank-$p$ Coxeter group $B_p$; for $p\geq2$ these models have two independent coupling constants, and a…

Let $A$ be an associative algebra with product $*$, and let $\pi_i\in A$ be idempotents satisfying … The idempotent construction produces an associative unital extension with compo…

Let $p$ be the rank of the Coxeter group $B_p$, and let rank-$p$ tensor boundary models be the tensor sigma-models whose fundamental field has tensor degree $p$. Coxeter $B_p$ tens…

The proposed Coxeter higher-spin theories are associated with free boundary conformal fields carrying tensorial higher-spin currents. Coxeter higher-spin holography conjecture. The…

Conjecture. Couplings of conserved currents to external potentials fulfill the higher order time-ordered $L,V_{\mu}$ relation. For $s=1$ the resulting field equations are quadratic…

The conjecture concerns the massless phase of a string theory emerging at an ultra-high energy regime, namely the “tensionless string” limit. Massless-phase conjecture. This phase…

Let $F_{\mu_1\nu_1,\dots,\mu_h\nu_h}$ denote a massive field with $h$ antisymmetric index pairs, and let the conclusions above refer to the extension of its time-ordered two-point…

The $O(N)$ or $U(N)$ scalar or fermion conformal field theories contain a tower of nearly conserved higher-spin currents $J_{\mu_1...\mu_s}(x)$, whose gauging gives a corresponding…

The paper studies higher-spin massive fermionic fields in $2+1$ dimensions. For spin $\frac{3}{2}$, the construction suggests that the nonlinear nature of the fields is compatible…

The paper constructs massive fermionic fields in $2+1$ dimensions and, for spin $\frac{3}{2}$, finds an underlying structure associated with the nonlinear behaviour of the boost op…

The framework uses a flat tensorial space with coordinates $X^A=(x^{\alpha\dot\alpha},z^{\alpha\beta},\bar z^{\dot\alpha\dot\beta})$ and a Maxwell algebra whose momentum commutator…

Brink–Metsaev–Vasiliev conjecture. An irreducible massless field in $AdS_d$ decomposes in the flat limit into a collection of irreducible massless fields in Minkowski spacetime.

Let ${\cal M}_4$ be the four-dimensional Siegel space, let $M^4\subset{\cal M}_4$ be its Minkowski-space submanifold, and let $Q_4$ denote the charge defined on ${\cal M}_4$. In Mi…