String-induced vacuum decay and its gravitational wave signatures

False vacuum decay typically proceeds via the nucleation of spherical bubbles of true vacuum, described by <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>O</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>4</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> symmetric field configurations in Euclidean time. In this work, we investigate how the presence of cosmic strings can catalyze the decay process. To this end, we consider a complex scalar field charged under a global or local <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>U</e:mi> <e:mo stretchy="false">(</e:mo> <e:mn>1</e:mn> <e:mo stretchy="false">)</e:mo> </e:math> symmetry. Assuming a nontrivial vacuum manifold, realizable for example in a simple sextic potential, we derive relativistic bounce solutions with <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>O</i:mi> <i:mo stretchy="false">(</i:mo> <i:mn>2</i:mn> <i:mo stretchy="false">)</i:mo> <i:mo>×</i:mo> <i:mi>O</i:mi> <i:mo stretchy="false">(</i:mo> <i:mn>2</i:mn> <i:mo stretchy="false">)</i:mo> </i:math> symmetry, corresponding to elongated bubbles seeded by a cosmic string of the same scalar field. Building up on earlier results in the literature, we identify the region of parameter space where vacuum decay predominantly proceeds via this alternative channel, thereby providing an explicit mechanism for the quantum decay of cosmic strings. Finally, we present an initial discussion of the gravitational wave signal associated with this type of vacuum decay and its possible connection to the recently observed stochastic signal in pulsar timing arrays.