Scale invariance vs conformal invariance

We find a large class of two-dimensional $$ \mathcal{N} $$
 = (0, 2) SCFTs obtained by compactifying four-dimensional $$ \mathcal{N} $$
 = 1 quiver gauge theories on a Riemann surface. We study these theories using anomalies and c-extremization. The gravitational duals to these fixed points are new AdS3 solutions of IIB supergravity which we exhibit explicitly. Along the way we uncover a universal relation between the conformal anomaly coefficients of fourdimensional and two-dimensional SCFTs connected by an RG flow across dimensions. We also observe an interesting novel phenomenon in which the superconformal R-symmetry mixes with baryonic symmetries along the RG flow.

/pdf/two-dimensional-scfts-from-d3-branes-1fro8w8dfe.pdf

Two-dimensional SCFTs from D3-branes

We construct supersymmetric AdS3 solutions in F-theory, that is Type IIB supergravity with varying axio-dilaton, which are holographically dual to 2d $$ \mathcal{N}=\left(0,4\right) $$
 superconformal field theories with small superconformal algebra. In F-theory these arise from D3-branes wrapped on curves in the base of an elliptically fibered Calabi-Yau threefold Y
 3 and correspond to self-dual strings in the 6d $$ \mathcal{N}=\left(1,0\right) $$
 theory obtained from F-theory on Y
 3. The non-trivial fibration over the wrapped curves implies a varying coupling of the $$ \mathcal{N}=4 $$
 Super-Yang-Mills theory on the D3-branes. We compute the holographic central charges and show that these agree with the field theory and with the anomalies of self-dual strings in 6d. We complement our analysis with a discussion of the dual M-theory solutions and a comparison of the central charges.

/pdf/f-theory-and-ads3-cft2-mpw6cojqlr.pdf

F-theory and AdS3/CFT2

We discuss walking behavior in gauge theories and weak first-order phase transitions in statistical physics. Despite appearing in very different systems (QCD below the conformal window, the Potts model, deconfined criticality) these two phenomena both imply approximate scale invariance in a range of energies and have the same RG interpretation: a flow passing between pairs of fixed point at complex coupling. We discuss what distinguishes a real theory from a complex theory and call these fixed points complex CFTs. By using conformal perturbation theory we show how observables of the walking theory are computable by perturbing the complex CFTs. This paper discusses the general mechanism while a companion paper [1] will treat a specific and computable example: the two-dimensional Q-state Potts model with Q > 4. Concerning walking in 4d gauge theories, we also comment on the (un)likelihood of the light pseudo-dilaton, and on non-minimal scenarios of the conformal window termination.

https://link.springer.com/content/pdf/10.1007/JHEP10(2018)108.pdf

Walking, Weak first-order transitions, and Complex CFTs

We compute 1/λ corrections to the four-point functions of half-BPS operators in SU(N) $$ \mathcal{N} $$
 = 4 super-Yang-Mills theory at large N and large ’t Hooft coupling λ = $$ {g}_{\mathrm{YM}}^2N $$
 using two methods. Firstly, we relate integrals of these correlators to derivatives of the mass deformed S4 free energy, which was computed at leading order in large N and to all orders in 1/λ using supersymmetric localization. Secondly, we use AdS/CFT to relate these 1/λ corrections to higher derivative corrections to supergravity for scattering amplitudes of Kaluza-Klein scalars in IIB string theory on AdS5× S5, which in the flat space limit are known from worldsheet calculations. These two methods match at the order corresponding to the tree level R4 interaction in string theory, which provides a precise check of AdS/CFT beyond supergravity, and allow us to derive the holographic correlators to tree level D4R4 order. Combined with constraints from [1], our results can be used to derive CFT data to one-loop D4R4 order. Finally, we use AdS/CFT to fix these correlators in the limit where N is taken to be large while gYM is kept fixed. In this limit, we present a conjecture for the small mass limit of the S4 partition function that includes all instanton corrections and is written in terms of the same Eisenstein series that appear in the study of string theory scattering amplitudes.

/pdf/mathcal-n-4-super-yang-mills-correlators-at-strong-coupling-3cfawn34f4.pdf

$\mathcal{N}=4$ Super-Yang-Mills Correlators at Strong Coupling from String Theory and Localization

Wend the gravity dual ofN = 2 � super-Yang-Mills theory on S 4 and use holography to calculate the universal contribution to the corresponding S 4 free energy at large N and large 't Hooft coupling. Our result matches the expression previously computed using supersymmetric localization in theeld theory. This match represents a non-trivial precision test of holography in a non-conformal, Euclidean signature setting.

/pdf/holography-for-n-1-on-s-4-4l4xwmcwcr.pdf

Holography for N=1*on S^4

We use maximal gauged supergravity in four dimensions to construct the gravity dual of a class of supersymmetric conformal interfaces in the theory on the worldvolume of multiple M2-branes. We study three classes of examples in which the (1+1)-dimensional defects preserve (4, 4), (0, 2) or (0, 1) supersymmetry. Many of the solutions have the maximally supersymmetric AdS
 4 vacuum dual to the $ \mathcal{N} $
 = 8 ABJM theory on both sides of the interface. We also find new special classes of solutions including one that interpolates between the maximally supersymmetric vacuum and a conformal fixed point with $ \mathcal{N} $
 = 1 supersymmetry and G2 global symmetry. We find another solution that interpolates between two distinct conformal fixed points with $ \mathcal{N} $
 = 1 supersymmetry and G2 global symmetry. In eleven dimensions, this G2 to G2 solution corresponds to a domain wall across which a magnetic flux reverses orientation.

/pdf/supersymmetric-janus-solutions-in-four-dimensions-2t6sqypmhf.pdf

Supersymmetric Janus solutions in four dimensions

We show that there is a family of two-dimensional (0, 2) SCFTs associated with twisted compactifications of the four-dimensional $ \mathcal{N} $
 = 1 Leigh-Strassler fixed point on a closed hyperbolic Riemann surface. We calculate the central charges for this class of theories using anomalies and c-extremization. In a suitable truncation of the five-dimensional maximal supergravity, we construct supersymmetric AdS
 3 solutions that are holographic duals of those two-dimensional (0, 2) SCFTs. We also exhibit supersymmetric domain wall solutions that are holographically dual to the RG flows between the four-dimensional and two-dimensional theories.

/pdf/0-2-scfts-from-the-leigh-strassler-fixed-point-3oz67brley.pdf

(0, 2) SCFTs from the Leigh-Strassler fixed point

We show that there is a family of two-dimensional $(0,2)$ SCFTs associated with twisted compactifications of the four-dimensional $\mathcal{N}=1$ Leigh-Strassler fixed point on a closed hyperbolic Riemann surface. We calculate the central charges for this class of theories using anomalies and $c$-extremization. In a suitable truncation of the five-dimensional maximal supergravity, we construct supersymmetric $AdS_3$ solutions that are holographic duals of those two-dimensional $(0,2)$ SCFTs. We also exhibit supersymmetric domain wall solutions that are holographically dual to the RG flows between the four-dimensional and two-dimensional theories.

/pdf/0-2-scfts-from-the-leigh-strassler-fixed-point-24c11wdbgb.pdf

(0,2) SCFTs from the Leigh-Strassler Fixed Point

We clarify the structure of the four-dimensional low-energy effective action that encodes the conformal and U(1) R-symmetry anomalies in an N = 1 supersymmetric field theory. The action depends on the dilaton, τ, associated with broken conformal symmetry, and the Goldstone mode, β, of the broken U(1) R-symmetry. We present the action for general curved spacetime and background gauge field up to and including all possible four- derivative terms. The result, constructed from basic principles, extends and clarifies the structure found by Schwimmer and Theisen in (1) using superfield methods. We show that the Goldstone mode β does not interfere with the proof of the four-dimensional a-theorem based on 2 → 2 dilaton scattering. In fact, supersymmetry Ward identities ensure that a proof of the a-theorem can also be based on 2 → 2 Goldstone mode scattering when the low- energy theory preserves N = 1 supersymmetry. We find that even without supersymmetry, a Goldstone mode for any broken global U(1) symmetry cannot interfere with the proof of the four-dimensional a-theorem.

/pdf/dilaton-effective-action-with-n-1-supersymmetry-393yyuygip.pdf

Nikolay Bobev

Papers

Holography for N=1*on S^4

Supersymmetric Janus solutions in four dimensions

(0, 2) SCFTs from the Leigh-Strassler fixed point

(0,2) SCFTs from the Leigh-Strassler Fixed Point

Dilaton effective action with N = 1 supersymmetry