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Register a new userConformal a-anomaly of some non-unitary 6d superconformal theories
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We compute the conformal anomaly a-coefficient for some non-unitary (higher derivative or non-gauge-invariant) 6d conformal fields and their supermultiplets. We use the method based on a connection between 6d determinants on S^6 and 7d determinants on AdS_7. We find, in particular, that (1,0) supermultiplet containing 4-derivative gauge-invariant conformal vector has precisely the value of a-anomaly as attributed in arXiv:1506.03807 (on the basis of R-symmetry and gravitational t Hooft matching) to the standard (1,0) vector multiplet. We also show that higher derivative (2,0) 6d conformal supergravity coupled to exactly 26 (2,0) tensor multiplets has vanishing a-anomaly. This is the 6d counterpart of the known fact of cancellation of the conformal anomaly in the 4d system of N=4 conformal supergravity coupled to 4 vector N=4 multiplets. In the case when 5 of tensor multiplets are chosen to be ghost-like and the conformal symmetry is spontaneously broken by a quadratic scalar constraint the resulting IR theory may be identified with (2,0) Poincare supergravity coupled to 21=26-5 tensor multiplets. The latter theory is known to be special: it is gravitational anomaly free and results upon compactification of 10d type IIB supergravity on K3.
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In arXiv:1510.02685 we proposed linear relations between the Weyl anomaly $c_1, c_2, c_3$ coefficients and the 4 coefficients in the chiral anomaly polynomial for (1,0) superconformal 6d theories. These relations were determined up to one free parameter $xi$ and its value was then conjectured using some additional assumptions. A different value for $xi$ was recently suggested in arXiv:1702.03518 using a different method. Here we confirm that this latter value is indeed the correct one by providing an additional data point: the Weyl anomaly coefficient $c_3$ for the higher derivative (1,0) superconformal 6d vector multiplet. This multiplet contains the 4-derivative conformal gauge vector, 3-derivative fermion and 2-derivative scalar. We find the corresponding value of $c_3$ which is proportional to the coefficient $C_T$ in the 2-point function of stress tensor using its relation to the first derivative of the Renyi entropy or the second derivative of the free energy on the product of thermal circle and 5d hyperbolic space. We present some general results of computation of the Renyi entropy and $C_T$ from the partition function on $S^1 times mathbb H^{d-1}$ for higher derivative conformal scalars, spinors and vectors in even dimensions. We also give an independent derivation of the conformal anomaly coefficients of the higher derivative vector multiplet from the Seeley-DeWitt coefficients on an Einstein background.
We construct and study the 6D dual superconformal algebra. Our construction is inspired by the dual superconformal symmetry of massless 4D $mathcal{N}=4$ SYM and extends the previous construction of the enhanced dual conformal algebra for 6D $mathcal{N}=(1,1)$ SYM to the full 6D dual superconformal algebra for chiral theories. We formulate constraints in 6D spinor helicity formalism and find all generators of the 6D dual superconformal algebra. Next we check that they agree with the dual superconformal generators of known 3D and 4D theories. We show that it is possible to significantly simplify the form of generators and compactly write the dual superconformal algebra using superindices. Finally, we work out some examples of algebra invariants.
We find and classify the ${cal N}=1$ SUSY multiplets on AdS$_4$ which contain partially massless fields. We do this by studying the non-unitary representations of the $d=3$ superconformal algebra of the boundary. The simplest super-multiplet which contains a partially massless spin-2 particle also contains a massless photon, a massless spin-$3/2$ particle and a massive spin-$3/2$ particle. The gauge parameters form a Wess-Zumino super-multiplet which contains the gauge parameters of the photon, the partially massless graviton, and the massless spin-$3/2$ particle. We find the AdS$_4$ action and SUSY transformations for this multiplet. More generally, we classify new types of shortening conditions that can arise for non-unitary representations of the $d=3$ superconformal algebra.
The trace anomaly in six-dimensional space is given by the local terms which have six derivatives of the metric. We find the effective action which is responsible for the anomaly. The result is presented in non-local covariant form and also in the local covariant form which employs two auxiliary scalar fields.
We find and classify the simplest ${cal N}=2$ SUSY multiplets on AdS$_4$ which contain partially massless fields. We do this by studying representations of the ${cal N}=2$, $d=3$ superconformal algebra of the boundary, including new shortening conditions that arise in the non-unitary regime. Unlike the ${cal N}=1$ case, the simplest ${cal N}=2$ multiplet containing a partially massless spin-2 is short, containing several exotic fields. More generally, we argue that ${cal N}=2$ supersymmetry allows for short multiplets that contain partially massless spin-$s$ particles of depth $t=s-2$.
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