Abstract
AbstractWe construct and study solitonic representations of the conformal net associated to some vacuum Positive Energy Representation (PER) of a loop group LG. For the corresponding solitonic states, we prove the Quantum Null Energy Condition (QNEC) and the Bekenstein Bound. As an intermediate result, we show that a Positive Energy Representation of a loop group LG can be extended to a PER of $$H^{s}(S^1,G)$$
H
s
(
S
1
,
G
)
for $$s>3/2$$
s
>
3
/
2
, where G is any compact, simple and simply connected Lie group. We also show the existence of the exponential map of the semidirect product $$LG \rtimes R$$
L
G
⋊
R
, with R a one-parameter subgroup of $$\mathrm{Diff}_+(S^1)$$
Diff
+
(
S
1
)
, and we compute the adjoint action of $$H^{s+1}(S^1,G)$$
H
s
+
1
(
S
1
,
G
)
on the stress energy tensor.
Funder
Università degli Studi di Roma La Sapienza
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
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