Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The interplay of the sign problem and the infinite volume limit: gauge
  theories with a theta term   QCD and related gauge theories have a sign problem when a $\theta$-term is
included; this complicates the extraction of physical information from
Euclidean space calculations as one would do in lattice studies. The sign
problem arises in this system because the partition function for configurations
with fixed topological charge $Q$, $\mathcal{Z}_Q$, are summed weighted by
$\exp(i Q \theta)$ to obtain the partition function for fixed $\theta$, $
\mathcal{Z}(\theta)$. The sign problem gets exponentially worse numerically as
the space-time volume is increased. Here it is shown that apart from the
practical numerical issues associated with large volumes, there are some
interesting issues of principle. A key quantity is the energy density as a
function of $\theta$, $\varepsilon(\theta) = -\log \left( \mathcal{Z}(\theta)
\right )/V$. This is expected to be well defined in the large 4-volume limit.
Similarly, one expects the energy density for a fixed topological density
$\tilde{\varepsilon}(Q/V) = -\log \left(\mathcal{Z}_Q \right )/V$ to be well
defined in the limit of large 4-volumes. Intuitively, one might expect that if
one had the infinite volume expression for $\tilde{\varepsilon}(Q/V)$ to
arbitrary accuracy, that one could reconstruct $\varepsilon(\theta)$ by
directly summing over the topological sectors of the partition function. We
show here that there are circumstances where this is not the case. In
particular, this occurs in regions where the curvature of $\varepsilon(\theta)$
is negative.

3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: math
9
The categories of this paper are: nlin