Lessons from the Ramond sector

Benjamin, Nathan; Lin, Ying-Hsuan

doi:10.21468/scipostphys.9.5.065

Cited by 31 publications

(21 citation statements)

References 44 publications

(160 reference statements)

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“…The partition function in this case is given by Z(τ ) = j(τ ) − 1728, which also arises as the Norton series for a certain pair of elements in the Monster group (see equation (73.4c) in [37, p. 425]). Although we do not have a direct physical interpretation for this problem, generalized modular transformations do arise in theories with discrete anomalies [38] or fermions [39,40], including sectors that obey Z(−1/τ ) = −Z(τ ).…”

Section: Uncertainty Principlementioning

confidence: 94%

High-dimensional sphere packing and the modular bootstrap

Afkhami-Jeddi

Cohn

Hartman

et al. 2020

J. High Energ. Phys.

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We carry out a numerical study of the spinless modular bootstrap for conformal field theories with current algebra U(1)c× U(1)c, or equivalently the linear programming bound for sphere packing in 2c dimensions. We give a more detailed picture of the behavior for finite c than was previously available, and we extrapolate as c → ∞. Our extrapolation indicates an exponential improvement for sphere packing density bounds in high dimen- sions. Furthermore, we study when these bounds can be tight. Besides the known cases c = 1/2, 4, and 12 and the conjectured case c = 1, our calculations numerically rule out sharp bounds for all other c < 90, by combining the modular bootstrap with linear programming bounds for spherical codes.

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Section: Uncertainty Principlementioning

confidence: 94%

High-dimensional sphere packing and the modular bootstrap

Afkhami-Jeddi

Cohn

Hartman

et al. 2020

J. High Energ. Phys.

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“…Our results naturally fall into the scope of conformal bootstrap program [25,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. We hope the techniques/functions used here would be useful in the broader context of this program, especially for the studies related to extremal functionals and dispersive sum rules [45][46][47][48][49] and its connection to analyticity in replica correlator [50].…”

Section: Jhep04(2021)288mentioning

confidence: 98%

Universality in asymptotic bounds and its saturation in 2D CFT

Das

Kusuki

Pal

2021

J. High Energ. Phys.

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We study asymptotics of three point coefficients (light-light-heavy) and two point correlators in heavy states in unitary, compact 2D CFTs. We prove an upper and lower bound on such quantities using numerically assisted Tauberian techniques. We obtain an optimal upper bound on the spectrum of operators appearing with fixed spin from the OPE of two identical scalars. While all the CFTs obey this bound, rational CFTs come close to saturating it. This mimics the scenario of bounds on asymptotic density of states and thereby pronounces an universal feature in asymptotics of 2D CFTs. Next, we clarify the role of smearing in interpreting the asymptotic results pertaining to considerations of eigenstate thermalization in 2D CFTs. In the context of light-light-heavy three point coefficients, we find that the order one number in the bound is sensitive to how close the light operators are from the $$ \frac{c}{32} $$ c 32 threshold. In context of two point correlator in heavy state, we find the presence of an enigmatic regime which separates the AdS3 thermal physics and the BTZ black hole physics. Furthermore, we present some new numerical results on the behaviour of spherical conformal block.

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“…This SPT phase arises, for example, as the infra-red limit of two Majorana fermions with masses of opposite sign and, in the condensed matter literature, it is better known as the topological phase of the Kitaev chain [5,8] . Recent applications of this topological field theory can found [9][10][11][12][13][14][15][16][17][18][19][20]. However, on a Riemann surface with boundary, the Arf topological field theory is not well defined: it suffers the same mod 2 anomaly that we saw above.…”

Section: The Mod 2 Anomalymentioning

confidence: 96%

Boundary RG flows for fermions and the mod 2 anomaly

Smith

Tong

2021

SciPost Phys.

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Boundary conditions for Majorana fermions in d=1+1d=1+1 dimensions fall into one of two SPT phases, associated to a mod 2 anomaly. Here we consider boundary conditions for 2N2N Majorana fermions that preserve a U(1)^NU(1)N symmetry. In general, the left-moving and right-moving fermions carry different charges under this symmetry, and implementation of the boundary condition requires new degrees of freedom, which manifest themselves in a boundary central charge gg. We follow the boundary RG flow induced by turning on relevant boundary operators. We identify the infra-red boundary state. In many cases, the boundary state flips SPT class, resulting in an emergent Majorana mode needed to cancel the anomaly. We show that the ratio of UV and IR boundary central charges is given by g^2_{IR} / g^2_{UV} = \mathrm{dim} \, \mathcal{O}gIR2/gUV2=dim𝒪, the dimension of the perturbing boundary operator. Any relevant operator necessarily has \mathrm{dim} \, \mathcal{O} < 1dim𝒪<1, ensuring that the central charge decreases in accord with the gg-theorem.

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Lessons from the Ramond sector

Cited by 31 publications

References 44 publications

High-dimensional sphere packing and the modular bootstrap

High-dimensional sphere packing and the modular bootstrap

Universality in asymptotic bounds and its saturation in 2D CFT

Boundary RG flows for fermions and the mod 2 anomaly

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