diff --git a/src/gt4py/next/program_processors/runners/dace/lowering/gtir_dataflow.py b/src/gt4py/next/program_processors/runners/dace/lowering/gtir_dataflow.py
index e7dc855428..e8d1914aa8 100644
--- a/src/gt4py/next/program_processors/runners/dace/lowering/gtir_dataflow.py
+++ b/src/gt4py/next/program_processors/runners/dace/lowering/gtir_dataflow.py
@@ -661,29 +661,31 @@ def _visit_deref(self, node: gtir.FunCall) -> DataExpr:
 
     def _visit_if_branch_arg(
         self,
-        if_sdfg: dace.SDFG,
-        if_branch_state: dace.SDFGState,
+        sdfg: dace.SDFG,
+        state: dace.SDFGState,
         param_name: str,
         arg: IteratorExpr | DataExpr,
         deref_on_input_memlet: bool,
-        if_sdfg_input_memlets: dict[str, MemletExpr | ValueExpr],
+        input_memlets: dict[str, MemletExpr | ValueExpr],
     ) -> IteratorExpr | ValueExpr:
         """
         Helper method to be called by `_visit_if_branch()` to visit the input arguments.
 
         Args:
-            if_sdfg: The nested SDFG where the if expression is lowered.
-            if_branch_state: The state inside the nested SDFG where the if branch is lowered.
+            sdfg: The SDFG where the if expression is lowered.
+            state: The state inside the given SDFG where the if branch is lowered.
             param_name: The parameter name of the input argument.
             arg: The input argument expression.
             deref_on_input_memlet: When True, the given iterator argument can be dereferenced on the input memlet.
-            if_sdfg_input_memlets: The memlets that provide input data to the nested SDFG, will be update inside this function.
+            input_memlets: The memlets that provide input data to the SDFG, will be updated inside this function.
         """
         use_full_shape = False
         if isinstance(arg, (MemletExpr, ValueExpr)):
+            field_dims = []
             arg_desc = arg.dc_node.desc(self.sdfg)
             arg_expr = arg
         elif isinstance(arg, IteratorExpr):
+            field_dims = [dim for dim, _ in arg.field_domain]
             arg_desc = arg.field.desc(self.sdfg)
             if deref_on_input_memlet:
                 # If the iterator is just dereferenced inside the branch state,
@@ -707,26 +709,39 @@ def _visit_if_branch_arg(
             inner_desc = arg_desc.clone()
             inner_desc.transient = False
         elif isinstance(arg.gt_dtype, ts.ScalarType):
-            inner_desc = dace.data.Scalar(arg_desc.dtype)
+            if isinstance(arg, MemletExpr) and len(arg.gt_field.dims) == 1:
+                # TODO(edopao): we cannot use a scalar because of an issue in gpu codegen,
+                # which leads to compilation error: cannot convert 'const double' to 'const double*'
+                inner_desc = dace.data.Array(dtype=arg_desc.dtype, shape=(1,))
+            else:
+                inner_desc = dace.data.Scalar(arg_desc.dtype)
         else:
             # for list of values, we retrieve the local size from the corresponding offset
-            assert arg.gt_dtype.offset_type is not None
-            offset_provider_type = self.subgraph_builder.get_offset_provider_type(
-                arg.gt_dtype.offset_type.value
+            local_dim = arg.gt_dtype.offset_type
+            assert local_dim is not None
+            assert isinstance(
+                self.subgraph_builder.get_offset_provider_type(local_dim.value),
+                gtx_common.NeighborConnectivityType,
             )
-            assert isinstance(offset_provider_type, gtx_common.NeighborConnectivityType)
+            # find position of the local dimension in the field layout
+            assert isinstance(arg_desc, dace.data.Array)
+            assert all(dim.kind != gtx_common.DimensionKind.LOCAL for dim in field_dims)
+            extended_dims = gtx_common.order_dimensions([*field_dims, local_dim])
+            local_dim_pos = extended_dims.index(local_dim)
             inner_desc = dace.data.Array(
-                dtype=arg_desc.dtype, shape=[offset_provider_type.max_neighbors]
+                dtype=arg_desc.dtype,
+                shape=(arg_desc.shape[local_dim_pos],),
+                strides=(arg_desc.strides[local_dim_pos],),
             )
 
-        if param_name in if_sdfg.arrays:
+        if param_name in sdfg.arrays:
             # the data desciptor was added by the visitor of the other branch expression
-            assert if_sdfg.data(param_name) == inner_desc
+            assert sdfg.data(param_name) == inner_desc
         else:
-            if_sdfg.add_datadesc(param_name, inner_desc)
-            if_sdfg_input_memlets[param_name] = arg_expr
+            sdfg.add_datadesc(param_name, inner_desc)
+            input_memlets[param_name] = arg_expr
 
-        inner_node = if_branch_state.add_access(param_name)
+        inner_node = state.add_access(param_name)
         if isinstance(arg, IteratorExpr) and use_full_shape:
             return IteratorExpr(inner_node, arg.gt_dtype, arg.field_domain, arg.indices)
         else:
@@ -734,10 +749,10 @@ def _visit_if_branch_arg(
 
     def _visit_if_branch(
         self,
-        if_sdfg: dace.SDFG,
-        if_branch_state: dace.SDFGState,
+        sdfg: dace.SDFG,
+        state: dace.SDFGState,
         expr: gtir.Expr,
-        if_sdfg_input_memlets: dict[str, MemletExpr | ValueExpr],
+        input_memlets: dict[str, MemletExpr | ValueExpr],
         direct_deref_iterators: Iterable[str],
     ) -> tuple[list[DataflowInputEdge], MaybeNestedInTuple[DataflowOutputEdge]]:
         """
@@ -746,10 +761,10 @@ def _visit_if_branch(
         This function is called by `_visit_if()` for each if-branch.
 
         Args:
-            if_sdfg: The nested SDFG where the if expression is lowered.
-            if_branch_state: The state inside the nested SDFG where the if branch is lowered.
+            sdfg: The SDFG where the if expression is lowered.
+            state: The state inside the given SDFG where the if branch is lowered.
             expr: The if branch expression to lower.
-            if_sdfg_input_memlets: The memlets that provide input data to the nested SDFG, will be update inside this function.
+            input_memlets: The memlets that provide input data to the SDFG, will be updated inside this function.
             direct_deref_iterators: Fields that are accessed with direct iterator deref, without any shift.
 
         Returns:
@@ -757,13 +772,17 @@ def _visit_if_branch(
                 - the list of input edges for the parent dataflow
                 - the tree representation of output data, in the form of a tuple of data edges.
         """
-        assert if_branch_state in if_sdfg.states()
+        assert state in sdfg.states()
 
-        lambda_args = []
-        lambda_params = []
+        lambda_args: list[MaybeNestedInTuple[IteratorExpr | DataExpr]] = []
+        lambda_params: list[gtir.Sym] = []
         for pname in symbol_ref_utils.collect_symbol_refs(expr, self.symbol_map.keys()):
             arg = self.symbol_map[pname]
-            if isinstance(arg, tuple):
+            inner_arg: MaybeNestedInTuple[IteratorExpr | DataExpr]
+            if isinstance(arg, SymbolExpr):
+                psymbol = im.sym(pname, gtx_dace_args.as_itir_type(arg.dc_dtype))
+                inner_arg = arg
+            elif isinstance(arg, tuple):
                 ptype = get_tuple_type(arg)  # type: ignore[arg-type]
                 psymbol = im.sym(pname, ptype)
                 psymbol_tree = gtir_to_sdfg_utils.make_symbol_tree(pname, ptype)
@@ -771,25 +790,25 @@ def _visit_if_branch(
                 inner_arg = gtx_utils.tree_map(
                     lambda tsym, targ, deref_on_input_memlet=deref_on_input_memlet: (
                         self._visit_if_branch_arg(
-                            if_sdfg,
-                            if_branch_state,
+                            sdfg,
+                            state,
                             str(tsym.id),
                             targ,
                             deref_on_input_memlet,
-                            if_sdfg_input_memlets,
+                            input_memlets,
                         )
                     )
                 )(psymbol_tree, arg)
             else:
-                psymbol = im.sym(pname, arg.gt_dtype)  # type: ignore[union-attr]
+                psymbol = im.sym(pname, arg.gt_dtype)
                 deref_on_input_memlet = pname in direct_deref_iterators
                 inner_arg = self._visit_if_branch_arg(
-                    if_sdfg,
-                    if_branch_state,
+                    sdfg,
+                    state,
                     pname,
                     arg,
                     deref_on_input_memlet,
-                    if_sdfg_input_memlets,
+                    input_memlets,
                 )
             lambda_args.append(inner_arg)
             lambda_params.append(psymbol)
@@ -797,7 +816,7 @@ def _visit_if_branch(
         # visit each branch of the if-statement as if it was a Lambda node
         lambda_node = gtir.Lambda(params=lambda_params, expr=expr)
         input_edges, output_tree = translate_lambda_to_dataflow(
-            if_sdfg, if_branch_state, self.subgraph_builder, lambda_node, lambda_args
+            sdfg, state, self.subgraph_builder, lambda_node, lambda_args
         )
 
         return input_edges, output_tree
@@ -818,9 +837,16 @@ def _visit_if_branch_result(
             # If the result is currently written to a transient node, inside the nested SDFG,
             # we need to allocate a non-transient data node.
             result_desc = edge.result.dc_node.desc(sdfg)
-            output_desc = result_desc.clone()
-            output_desc.transient = False
-            output_data = sdfg.add_datadesc(output_data, output_desc, find_new_name=True)
+            if isinstance(sym.type, ts.ScalarType) and isinstance(result_desc, dace.data.Array):
+                # TODO(edopao): a scalar should not be represented as an array, but
+                # currently this can happen because of an issue workaround, see the
+                # todo comment above in `_visit_if_branch_arg()`.
+                assert len(result_desc.shape) == 1 and result_desc.shape[0] == 1
+                _, output_desc = sdfg.add_scalar(output_data, result_desc.dtype)
+            else:
+                output_desc = result_desc.clone()
+                output_desc.transient = False
+                output_data = sdfg.add_datadesc(output_data, output_desc, find_new_name=True)
         output_node = state.add_access(output_data)
         state.add_nedge(
             edge.result.dc_node,
@@ -868,6 +894,13 @@ def write_output_of_nested_sdfg_to_temporary(inner_value: ValueExpr) -> ValueExp
         nsdfg = dace.SDFG(self.subgraph_builder.unique_nsdfg_name("if_stmt"))
         nsdfg.debuginfo = gtir_to_sdfg_utils.debug_info(node, default=self.sdfg.debuginfo)
 
+        # add connectivities
+        for aname, adesc in self.sdfg.arrays.items():
+            if gtx_dace_args.is_connectivity_identifier(aname):
+                adesc = adesc.clone()
+                adesc.transient = True
+                nsdfg.add_datadesc(aname, adesc)
+
         # create states inside the nested SDFG for the if-branches
         if_region = dace.sdfg.state.ConditionalBlock("if")
         nsdfg.add_node(if_region, ensure_unique_name=True)
@@ -948,14 +981,21 @@ def write_output_of_nested_sdfg_to_temporary(inner_value: ValueExpr) -> ValueExp
 
         outputs = {outval.dc_node.data for outval in gtx_utils.flatten_nested_tuple((result,))}
 
+        # map the connectivities that were used inside the nested SDFG
+        used_connectivities = [
+            aname
+            for aname, adesc in nsdfg.arrays.items()
+            if gtx_dace_args.is_connectivity_identifier(aname) and not adesc.transient
+        ]
+
         # all free symbols are mapped to the symbols available in parent SDFG
         nsdfg_symbols_mapping = {str(sym): sym for sym in nsdfg.free_symbols}
         if isinstance(condition_value, SymbolExpr):
             nsdfg_symbols_mapping["__cond"] = condition_value.value
         nsdfg_node = self.state.add_nested_sdfg(
             nsdfg,
-            inputs=set(input_memlets.keys()),
-            outputs=outputs,
+            inputs=sorted(used_connectivities | input_memlets.keys()),
+            outputs=sorted(outputs),
             symbol_mapping=nsdfg_symbols_mapping,
         )
 
@@ -971,6 +1011,16 @@ def write_output_of_nested_sdfg_to_temporary(inner_value: ValueExpr) -> ValueExp
                     self.sdfg.make_array_memlet(input_expr.dc_node.data),
                 )
 
+        for conn in used_connectivities:
+            desc = self.sdfg.data(conn)
+            desc.transient = False
+            self._add_input_data_edge(
+                self.state.add_access(conn),
+                dace_subsets.Range.from_array(desc),
+                nsdfg_node,
+                conn,
+            )
+
         return (
             gtx_utils.tree_map(write_output_of_nested_sdfg_to_temporary)(result)
             if isinstance(result, tuple)
@@ -1904,6 +1954,9 @@ def visit_Literal(self, node: gtir.Literal) -> SymbolExpr:
         dc_dtype = gtx_dace_args.as_dace_type(node.type)
         return SymbolExpr(node.value, dc_dtype)
 
+    def visit_OffsetLiteral(self, node: gtir.OffsetLiteral) -> SymbolExpr:
+        return SymbolExpr(node.value, gtir_to_sdfg_types.INDEX_DTYPE)
+
     def visit_SymRef(self, node: gtir.SymRef) -> MaybeNestedInTuple[IteratorExpr | DataExpr]:
         param = str(node.id)
         if param in self.symbol_map:
@@ -1918,7 +1971,7 @@ def translate_lambda_to_dataflow(
     state: dace.SDFGState,
     sdfg_builder: gtir_to_sdfg.DataflowBuilder,
     node: gtir.Lambda,
-    args: Sequence[MaybeNestedInTuple[IteratorExpr | MemletExpr | ValueExpr]],
+    args: Sequence[MaybeNestedInTuple[IteratorExpr | DataExpr]],
 ) -> tuple[list[DataflowInputEdge], MaybeNestedInTuple[DataflowOutputEdge]]:
     """
     Entry point to visit a `Lambda` node and lower it to a dataflow graph,