49 research outputs found

### Universality of radiative corrections to gauge couplings for strings with spontaneously broken supersymmetry

I review recent work on computing radiative corrections to non-abelian gauge
couplings in four-dimensional heterotic vacua with spontaneously broken
supersymmetry. The prototype models can be considered as K3 surfaces with
additional Scherk-Schwarz fluxes inducing the spontaneous $\mathcal{N}=2 \to
\mathcal{N}=0$ breaking. Remarkably, although the gauge thresholds are no
longer BPS protected and receive contributions also from the excitations of the
RNS sector, their difference is still exactly computable and universal. Based
on a talk presented at the DISCRETE 2014 conference at King's College London.Comment: 18 pages, corrected eq. 4.16 and an overall factor of

### A Solution to the Decompactification Problem in Chiral Heterotic Strings

We present a solution to the decompactification problem of gauge thresholds
in chiral heterotic string theories with two large extra dimensions, where
supersymmetry is spontaneously broken by the Scherk-Schwarz mechanism. Whenever
the Kaluza-Klein scale is much lower than the string scale, the infinite towers
of heavy states contribute non-trivially to the renormalisation of gauge
couplings, which typically grow linearly with the large volume of the internal
space and invalidate perturbation theory. We trace the origin of the
decompactification problem to properties of the six dimensional theory obtained
in the infinite volume limit and show that thresholds may instead exhibit
logarithmic volume dependence and we provide the conditions for this to occur.
We illustrate this mechanism with explicit string constructions where the
decompactification problem does not occur.Comment: 26 pages, 1 figur

### On the Rankin-Selberg method for higher genus string amplitudes

Closed string amplitudes at genus $h\leq 3$ are given by integrals of Siegel
modular functions on a fundamental domain of the Siegel upper half-plane. When
the integrand is of rapid decay near the cusps, the integral can be computed by
the Rankin-Selberg method, which consists of inserting an Eisenstein series
$E_h(s)$ in the integrand, computing the integral by the orbit method, and
finally extracting the residue at a suitable value of $s$. String amplitudes,
however, typically involve integrands with polynomial or even exponential
growth at the cusps, and a renormalization scheme is required to treat infrared
divergences. Generalizing Zagier's extension of the Rankin-Selberg method at
genus one, we develop the Rankin-Selberg method for Siegel modular functions of
degree 2 and 3 with polynomial growth near the cusps. In particular, we show
that the renormalized modular integral of the Siegel-Narain partition function
of an even self-dual lattice of signature $(d,d)$ is proportional to a residue
of the Langlands-Eisenstein series attached to the $h$-th antisymmetric tensor
representation of the T-duality group $O(d,d,Z)$.Comment: 53 pages, 3 figures; v2: various clarifications and cosmetic changes,
new appendix B on the Rankin-Selberg transform of the lattice partition
function in arbitrary degree, small correction to Figure

### $\mathcal{N}=2^\star$ from Topological Amplitudes in String Theory

In this paper, we explicitly construct string theory backgrounds that realise
the so-called $\mathcal N=2^\star$ gauge theory. We prove the consistency of
our models by calculating their partition function and obtaining the correct
gauge theory spectrum. We further provide arguments in favour of the
universality of our construction which covers a wide class of models all of
which engineer the same gauge theory. We reproduce the corresponding Nekrasov
partition function once the $\Omega$-deformation is included and the
appropriate field theory limit taken. This is achieved by calculating the
topological amplitudes $F_g$ in the string models. In addition to heterotic and
type II constructions, we also realise the mass deformation in type I theory,
thus leading to a natural way of uplifting the result to the instanton sector.Comment: 27 page

### Higher Spins in Hyperspace

We consider the Sp(2n) invariant formulation of higher spin fields on flat
and curved backgrounds of constant curvature.In this formulation an infinite
number of higher spin fields are packed into single scalar and spinor master
fields (hyperfields) propagating on extended spaces, to be called hyperspaces,
parametrized by tensorial coordinates.We show that the free field equations on
flat and AdS-like hyperspaces are related to each other by a generalized
conformal transformation of the scalar and spinor master fields. We compute the
four--point functions on a flat hyperspace for both scalar and spinor master
fields, thus extending the two-- and three--point function results of
arXiv:hep-th/0312244. Then using the generalized conformal transformation we
derive two--, three-- and four--point functions on AdS--like hyperspace from
the corresponding correlators on the flat hyperspace.Comment: 23 pages, typos corrected, references added. Published versio

### Marginal Deformations of Vacua with Massive boson-fermion Degeneracy Symmetry

Two-dimensional string vacua with Massive Spectrum boson-fermion Degeneracy
Symmetry (MSDS) are explicitly constructed in Type II and Heterotic superstring
theories. The study of their moduli space indicates the existence of large
marginal deformations that connect continuously the initial d=2, MSDS vacua to
higher-dimensional conventional superstring vacua, where spacetime
supersymmetry is spontaneously broken by geometrical fluxes. We find that the
maximally symmetric, d=2, Type II MSDS-vacuum, is in correspondence with the
maximal, N=8, d=4, gauged supergravity, where the supergravity gauging is
induced by the fluxes. This correspondence is extended to less symmetric cases
where the initial MSDS symmetry is reduced by orbifolds. We also exhibit and
analyse thermal interpretations of some Euclidean versions of the models and
identify classes of MSDS vacua that remain tachyon-free under arbitrary
marginal deformations about the extended symmetry point. The connection between
the two-dimensional MSDS vacua and the resulting four-dimensional effective
supergravity theories arises naturally within the context of an adiabatic
cosmological evolution, where the very early Universe is conjectured to be
described by an MSDS-vacuum, while at late cosmological times it is described
by an effective N=1 supergravity theory with spontaneously broken
supersymmetry

### Rankin-Selberg methods for closed strings on orbifolds

In recent work we have developed a new unfolding method for computing
one-loop modular integrals in string theory involving the Narain partition
function and, possibly, a weak almost holomorphic elliptic genus. Unlike the
traditional approach, the Narain lattice does not play any role in the
unfolding procedure, T-duality is kept manifest at all steps, a choice of Weyl
chamber is not required and the analytic structure of the amplitude is
transparent. In the present paper, we generalise this procedure to the case of
Abelian Z_N orbifolds, where the integrand decomposes into a sum of orbifold
blocks that can be organised into orbits of the Hecke congruence subgroup
{\Gamma}_0(N). As a result, the original modular integral reduces to an
integral over the fundamental domain of {\Gamma}_0(N), which we then evaluate
by extending our previous techniques. Our method is applicable, for instance,
to the evaluation of one-loop corrections to BPS-saturated couplings in the low
energy effective action of closed string models, of quantum corrections to the
K\"ahler metric and, in principle, of the free-energy of superstring vacua.Comment: 47 pages, 1 figur

### One-Loop BPS amplitudes as BPS-state sums

Recently, we introduced a new procedure for computing a class of one-loop
BPS-saturated amplitudes in String Theory, which expresses them as a sum of
one-loop contributions of all perturbative BPS states in a manifestly T-duality
invariant fashion. In this paper, we extend this procedure to all BPS-saturated
amplitudes of the form \int_F \Gamma_{d+k,d} {\Phi}, with {\Phi} being a weak
(almost) holomorphic modular form of weight -k/2. We use the fact that any such
{\Phi} can be expressed as a linear combination of certain absolutely
convergent Poincar\'e series, against which the fundamental domain F can be
unfolded. The resulting BPS-state sum neatly exhibits the singularities of the
amplitude at points of gauge symmetry enhancement, in a chamber-independent
fashion. We illustrate our method with concrete examples of interest in
heterotic string compactifications.Comment: 42 pages; v4: a few misprints correcte

### Universality of Gauge Thresholds in Non-Supersymmetric Heterotic Vacua

We compute one-loop threshold corrections to non-abelian gauge couplings in
four-dimensional heterotic vacua with spontaneously broken $\cal N = 2 \to \cal
N = 0$ supersymmetry, obtained as Scherk-Schwarz reductions of six-dimensional
K3 compactifications. As expected, the gauge thresholds are no-longer BPS
protected, and receive contributions also from the excitations of the RNS
sector. Remarkably, the difference of thresholds for non-abelian gauge
couplings is BPS saturated and exhibits a universal behaviour independently of
the orbifold realisation of K3. Moreover, the thresholds and their difference
develop infra-red logarithmic singularities whenever charged BPS-like states,
originating from the twisted RNS sector, become massless at special loci in the
classical moduli space.Comment: 12 pages, corrected eqs. 3.19, 3.20 and 3.23 and an overall factor of
2 in all threshold